{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Text provided under a Creative Commons Attribution license, CC-BY.  All code is made available under the FSF-approved BSD-3 license.  (c) Lorena A. Barba, Gilbert F. Forsyth 2017. Thanks to NSF for support via CAREER award #1149784."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[@LorenaABarba](https://twitter.com/LorenaABarba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12 steps to Navier–Stokes\n",
    "=====\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a moment, recall the Navier–Stokes equations for an incompressible fluid, where $\\vec{v}$ represents the velocity field:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray*}\n",
    "\\nabla \\cdot\\vec{v} &=& 0 \\\\\n",
    "\\frac{\\partial \\vec{v}}{\\partial t}+(\\vec{v}\\cdot\\nabla)\\vec{v} &=& -\\frac{1}{\\rho}\\nabla p + \\nu \\nabla^2\\vec{v}\n",
    "\\end{eqnarray*}\n",
    "$$\n",
    "\n",
    "The first equation represents mass conservation at constant density. The second equation is the conservation of momentum. But a problem appears: the continuity equation for incompressble flow does not have a dominant variable and there is no obvious way to couple the velocity and the pressure. In the case of compressible flow, in contrast, mass continuity would provide an evolution equation for the density $\\rho$, which is coupled with an equation of state relating $\\rho$ and $p$.\n",
    "\n",
    "In incompressible flow, the continuity equation $\\nabla \\cdot\\vec{v}=0$ provides a *kinematic constraint* that requires the pressure field to evolve so that the rate of expansion $\\nabla \\cdot\\vec{v}$ should vanish everywhere. A way out of this difficulty is to *construct* a pressure field that guarantees continuity is satisfied; such a relation can be obtained by taking the divergence of the momentum equation. In that process, a Poisson equation for the pressure shows up!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 10: 2D Poisson Equation\n",
    "----\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Poisson's equation is obtained from adding a source term to the right-hand-side of Laplace's equation:\n",
    "\n",
    "$$\\frac{\\partial ^2 p}{\\partial x^2} + \\frac{\\partial ^2 p}{\\partial y^2} = b$$\n",
    "\n",
    "So, unlinke the Laplace equation, there is some finite value inside the field that affects the solution. Poisson's equation acts to \"relax\" the initial sources in the field.\n",
    "\n",
    "In discretized form, this looks almost the same as [Step 9](./12_Step_9.ipynb), except for the source term:\n",
    "\n",
    "$$\\frac{p_{i+1,j}^{n}-2p_{i,j}^{n}+p_{i-1,j}^{n}}{\\Delta x^2}+\\frac{p_{i,j+1}^{n}-2 p_{i,j}^{n}+p_{i,j-1}^{n}}{\\Delta y^2}=b_{i,j}^{n}$$\n",
    "\n",
    "As before, we rearrange this so that we obtain an equation for $p$ at point $i,j$. Thus, we obtain:\n",
    "\n",
    "$$p_{i,j}^{n}=\\frac{(p_{i+1,j}^{n}+p_{i-1,j}^{n})\\Delta y^2+(p_{i,j+1}^{n}+p_{i,j-1}^{n})\\Delta x^2-b_{i,j}^{n}\\Delta x^2\\Delta y^2}{2(\\Delta x^2+\\Delta y^2)}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will solve this equation by assuming an initial state of $p=0$ everywhere, and applying boundary conditions as follows:\n",
    "\n",
    "$p=0$ at $x=0, \\ 2$ and $y=0, \\ 1$\n",
    "\n",
    "and the source term consists of two initial spikes inside the domain, as follows:\n",
    "\n",
    "$b_{i,j}=100$ at $i=\\frac{1}{4}nx, j=\\frac{1}{4}ny$\n",
    "\n",
    "$b_{i,j}=-100$ at $i=\\frac{3}{4}nx, j=\\frac{3}{4}ny$\n",
    "\n",
    "$b_{i,j}=0$ everywhere else.\n",
    "\n",
    "The iterations will advance in pseudo-time to relax the initial spikes. The relaxation under Poisson's equation gets slower and slower as they progress. *Why?*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at one possible way to write the code for Poisson's equation. As always, we load our favorite Python libraries. We also want to make some lovely plots in 3D. Let's get our parameters defined and the initialization out of the way. What do you notice of the approach below?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "from matplotlib import pyplot, cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters\n",
    "nx = 50\n",
    "ny = 50\n",
    "nt  = 100\n",
    "xmin = 0\n",
    "xmax = 2\n",
    "ymin = 0\n",
    "ymax = 1\n",
    "\n",
    "dx = (xmax - xmin) / (nx - 1)\n",
    "dy = (ymax - ymin) / (ny - 1)\n",
    "\n",
    "# Initialization\n",
    "p  = numpy.zeros((ny, nx))\n",
    "pd = numpy.zeros((ny, nx))\n",
    "b  = numpy.zeros((ny, nx))\n",
    "x  = numpy.linspace(xmin, xmax, nx)\n",
    "y  = numpy.linspace(xmin, xmax, ny)\n",
    "\n",
    "# Source\n",
    "b[int(ny / 4), int(nx / 4)]  = 100\n",
    "b[int(3 * ny / 4), int(3 * nx / 4)] = -100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With that, we are ready to advance the initial guess in pseudo-time. How is the code below different from the function used in [Step 9](./12_Step_9.ipynb) to solve Laplace's equation?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "for it in range(nt):\n",
    "\n",
    "    pd = p.copy()\n",
    "\n",
    "    p[1:-1,1:-1] = (((pd[1:-1, 2:] + pd[1:-1, :-2]) * dy**2 +\n",
    "                    (pd[2:, 1:-1] + pd[:-2, 1:-1]) * dx**2 -\n",
    "                    b[1:-1, 1:-1] * dx**2 * dy**2) / \n",
    "                    (2 * (dx**2 + dy**2)))\n",
    "\n",
    "    p[0, :] = 0\n",
    "    p[ny-1, :] = 0\n",
    "    p[:, 0] = 0\n",
    "    p[:, nx-1] = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maybe we could reuse our plotting function from [Step 9](./12_Step_9.ipynb), don't you think?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot2D(x, y, p):\n",
    "    fig = pyplot.figure(figsize=(11, 7), dpi=100)\n",
    "    ax = fig.gca(projection='3d')\n",
    "    X, Y = numpy.meshgrid(x, y)\n",
    "    surf = ax.plot_surface(X, Y, p[:], rstride=1, cstride=1, cmap=cm.viridis,\n",
    "            linewidth=0, antialiased=False)\n",
    "    ax.view_init(30, 225)\n",
    "    ax.set_xlabel('$x$')\n",
    "    ax.set_ylabel('$y$')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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Eo3Rc9FAULh38uHUxXr3mh0lvRi4RKy/56J1fai8qiphyZfscxX7z3ndAuGMopmf5oAWA\nkehd0Y5TlJCgSwDR1HdcTzg+jUoRnGzgVZBCx3A60Oc7ICmR4+WbllT0Lo/E+ePb7xiK6VmGLHrH\n7mnseUrPjg8Juikga60VNo3K3s9C4Um0ZipqhG7S/eaP/7gFKdOiiMd4bXt30ptQWMTonVfXg0mi\nd2zecdGYxrVFdQzZ/Dv+ddHehhd41JpsckjQxcC4rbXYe2V2FGkyhS1i+iIM/K9O9o/9omVRB/r8\nkoeda4wXXjwPzfVPUNuzBBEn5qsiP2m5FqaZpK7TquKKTqczVnGFqjUZP5YYQFeuiIiitVbaPeHS\nsh3TJkjUKktRuCJjWRYsy3Ii5aVSCd82DADA82YNtVXhwG4c7P95JO0/zPwiP2Gid2nf1zhIwz7L\nvO+CFsjIBB61JvOGBN2YTNJaKwpPuKRg4ibN2zgNvOYzTmILQ0SLrOgEGJxv9Xp9cIw6w/Hr16+H\nZVlotVowTRMLCwvOhHAyzE0WWeSHpWa95m0B6RA30yaN++wl0lmKnT+OQbzvGJSeJUEXGFk1KiNo\nFC5qTzhiusiicEnNZyTUyOx7+KKTTqfjebzYeCb62NxXsd1VlpvVZx0+8gOo522xtldFJI2CTsQr\nPTtOazI+Pcvuy3FVTqeRYn7TAyJLoxqG4UTTvL4kee2tWaRJ80yI82k6XojnORWXJWQ/mIK2QWu0\nLvZctspyQ7zhsO9DVs/rrONnistu7uz8LQJZEHQ8svRs0O4jMoG3vLwMXdedrFcRWpORoPPg7W9/\nO+6//34AGMnTi18I8hPLB7J0OLsZFOE4ZkWwi8eJXbAn/cH0wovn4eyznla+rmp3tbS0BACuG07a\nvytZu+EHRWaKu7i4CNM0sbi46BLpWThO45KF89gLTVN3HwnifQfAFdVj0Ts2Po/kc68igrWs4ZH5\n5xTJEy4rN/ygqI4jS6Xquu6k2PN4PLNCkOMUBc+bNZwdcCx/w5Gli3jRUJSoUBph1+LZ2VmUSiXP\n45Sn63beBHsY7ztd10eMldnfvGZWABJ0nmia5qpyE9NvUbfWIqaD6O1HxzGdZGnOoiwqNG5FJhEf\nsuPEhIHomZaH6F3Wt19FEO8727adH315FnE8JOg8WLduHb761a/iX//1X3HppZdiz549zi+4er1e\nmC8JTxYjdKqilKijO8TkiL1s4ywe8ps/Nwl+FZlp6IaQtwiOF6p95Vtazc7OBp6UnwWKZKYsnm8s\nzc6OJX8cmQjMIyToOGzbxve//338/d//Pf7u7/4OjzzyCE6ePIk3v/nNOO+889BoNJwTvignikhW\nBF2UUbis7HNUTHNfVXNPp2Xhwzzo4kRVkcnPBSJblHgJIl79JuUDNEcyC7D5tACwdu1aaJrm8r6b\nmZlJeAvjI9WC7tChQ7jttttgWRauu+467N27d2TMLbfcgoceegiNRgP79u3Drl27AAALCwu4/vrr\n8f3vfx+6ruPee+/Fnj17lOtqtVq44IILUKvV8Ku/+qv44Ac/iJe//OX4rd/6LVx00UWx7SMRDapK\nx7xXpEbNNG4AfrYiSd+EXnjxPKxtPB7b8lXdEERblCKlitKIOEeSCfGsRO+KKugY/Bw6PjKX53Mq\ntYLOsizcfPPNOHz4MM4991zs3r0bV1xxBXbs2OGMeeihh/DUU0/hiSeewKOPPoqbbroJR44cAQDc\neuutuOyyy/D5z38e/X4fKysrnutrNBr4t3/7N7z0pS91nnvsscdw5swZ17iiRWtE0rT/ebWGyRte\ntiJprBx+3qxh7ZTWxd9s+JRft9slW5QImVTc8LYXYoVzWoV4kQWd6h6VZ8sSIMWC7ujRo9i+fTu2\nbdsGALj66qtx4MABl6A7cOAArrnmGgDAnj17sLCwgJMnT6Jer+Nf/uVfsG/fPgCDidTr1q3zXScv\n5gCg2Wzi9OnTrufSJGiKhqrPbRC/sUmgYx4e3laET3mnRWyv76qj9UkyTVuUotzw4zh3VZYaohBP\nMnpXlOMrQ6xwLQqpFXQnTpzA1q1bncdbtmzB0aNHPcfMz8/jxIkTKJVKOOuss/D+978f3/3ud3HJ\nJZfg05/+NOr1eqht2LBhA0XoBFjl77SgKFw2mJatSJEgW5RoifNaESR6N+0imCLfp4oqZnN5le33\n+/jOd76D3/7t38Z3vvMdzM7O4o477gi9nGazOSLoGEU9WeIWtCyy0+120Wq10G63YZomyuUyGo0G\nZmdnUavVpvqrt2giPui+smPV6XSwsrKCTqcD27ZRrVbRaDRQr9cTreLME2zCfr1ex7p16zA3N4dq\ntYp+v4/FxUUsLCxgZWXF6WhDDJn258GEeKPRwNzcHNatW4dyuQzDMHDmzBksLCw4HSzi3rYiihpg\nEAiQ7XveP4/URujm5+fx7LPPOo+PHz+O+fn5kTHHjh2Tjtm6dSsuueQSAMA73/lO3HnnnaG3odls\nYmFhwfVc3r8QSSBaVaRtknyR8Pusp2krQqiJwhalSFGMJPdTZYjbarVitbAp0vEVKZJlC09qBd3u\n3bvx5JNP4plnnsHmzZuxf/9+pw0X4/LLL8fdd9+Nq666CkeOHMHc3Bw2bdoEYCDofvSjH+GCCy7A\n4cOHceGFF4beBlWEjkVsiniyRBGtojZp2SFpW5GkeGJxF85f+x9Jb0YgyBbFmzRdq1W9gYO0swoD\na1aflv2eNqp9z/vnkVpBVyqVcNddd+HSSy91bEt27tyJe+65B5qm4cYbb8Rll12GgwcP4vzzz0ej\n0cB9993nvP/P/uzP8J73vAe9Xg8vf/nLXa8FxU/QEcFgF5esRuGKdrzZHKC02opMylnW/wlgOh50\nSRDUFqVI3+m04tfOatLoXdbP1XEpqpjVfE7qQp/xnU4H73jHO/ClL33J9Xy73c51g18vLMtCu91G\no9HwHCdr28SicFmLEti2jVarhTVr1iS9KbHA24qweT3sOOWxTRXrEOEn6M5f+x+YnZ2dxiZNDRYR\nYv/SUI0ZN/1+H61WC+vXr096U0LBR1pZpXjQ6J1lWVhYWECz2ZziFqeHdrsN27ZHzl92Xcs4ygNf\nPEUSgpmZGXS73aQ3IxPwVY7i/Kq8NL3O068+la1IpVJBr9fLtZt6keEjQqdOncLMzExmOyHkHVWk\nVWxGL6siz9O1ahyKuv8k6HxQ5eGLmq7g910Vhcvb/Ko87EdQWxF+rlwe+cvj/wOvb3Swq0qCFYAr\n/ZpXW5Q83Nz9mtGL0bs87PMkMMErkvfPhATdGBRV0DFRAMD5lUhVjulFJriZgMtres2P1zf+d+Cx\nTy79Al49+8MYtyY5xOuX2MdUFAzMimPSyfpJkEdx41flXCqVnB9wWRbj40JVroQUZqTLfzmKJOhk\nogBAJi/sk5CVymYvW5EiXuAm4ZxS/qdbqL7PfoKB/TAgn8HkkVU5dzodmKaJxcVFJ7rH2pKl/RoW\nBVm4VscBCTof1q5di8XFRczNzTnPTbtbwjRRpeZ4UdBqtQob4UkbRbUVGYdBujXprcgeKlsUNp+L\npfvSGvkt2s2dVaWbpok1a9Y4qXRmZpyXVLoXZFtCSGHWJbygyxuipQhAqbk0I2uHlidbkWnwmNFB\nkEY5L7x4Hs4+6+nYtydLqCbrx22USwSH72Xql0rPYyFM0UQ8gwSdD3ns5zpp382s7/84JLnPvK2I\naZpOyisOI+a8Htu/PP4/kt6EVBHVDc/LKLfVaqXCFqWIN3fVPstS6apCmCz/OCziMQdI0PkiMxfO\n4k2PtxThbSrGjcJlbf+zhspWpFarZfpCmyR8QYTpE50rwvy5OPBqUg+QLcq0CCJoZNE7Fm3NcvRO\n1SWjCEV7JOh8yKqgk0V1wkThvMj7SSEj7mM+adSUiI9PP3Ulbn3Fl5PejMzBKmOZLYplWTAMY+q2\nKEWM1oyzz6xFXLVaxezs7Ej0TvS9S+tnyqebiwYJOh82btyI06dPu55Lq6CLOgqnIq37nzXIVmQ6\nTJpu/c31j0W0JcVF0zSUSiXU63VXNMgwjNhtUYoq6Cb90c5H7/ho69LSEoD0RluLeLwZJOh8aDab\n+MlPfiJ9LekvTpxROCJ6ZD1tyVaESIKkr118NIify0W2KNEQ9Q9uv2hrGuZKMopa4QqQoPOl2Wxi\nYWHB9VySXwxZheO051YVMUI37j5nzVYkb8eWRefCGApfXK3ihOmeQ0dp1/jwqsSMwhalqCazcV1b\nxGirOFfStm2X7920P/ukf6wkCQk6H5rN5kjKFZie0SwvCMQKRybiiHRBtiL5g9Ku04NsUSZnmqJG\nFr3r9XrodruJRO8oQkcokRVFAPFGMtIQhfMib1GcIHjt8zRtRYjgfOiHv4Ofi9BIeGlpKTdpwKxE\nMaKwRcnKvkZJUvvMoneqSmcWvYtTkIudnYoECTofVIIOiG6egiotl1ZBkOdOGUEhW5H0wQvrjzz9\n+/i5xn9Huvx7X3gvrj37r500IBN3Sc8ZKhLj2KIU7ccnkB4Ry0fvgFFBzuYPR3keUYSOUFKr1WAY\nxsjzk345xJ6blJZLN6ygwTAMshVJESphzSPOn/PzoAOA+dJanDCXRp5fu3ats07DMMhfLUGCTNRn\nrxXtmKR1n0VBHkc6Pa37Pg1I0I1J2LRj1qJwXhQl5crbirBjluaelVHARzXSun/ijyFRWA9SreNF\n5/5xeSf+kXvMz537zfWPYec9d+HxD9zs3HREt32WBkx7ajZv569qoj77AdZqtdDr9QrToD7N5y/D\nK53OF8OEtbJRFcGk/fOIAhJ0AVCFb70uijKLCorCpRsvWxF20anVaglvZfEIUyn8oR/+TqTrvn9h\nl0vUvfY1P8DOe+5yHj/+gZt9KzTTmppN07ZEDR+9W1hYcAoseFsU3iQ3b2RB0ImoonfsmAWN3mVx\n36OCBF0A2Jwx/kskE3RZs6gYlzxF6IIeM8MwcrPPWUCWSlX9GLrovv/X+f+bfhm+0bn/6/jbcPuW\nhwJviyjqeHhxBwwEnlihSanZ5PFqUD9uJCit5OE6JUbv2DELEr2zLCvzx3BcSNAFYP369VhcXMTc\n3JzrebG6kY/oUBQuvYxjK0KFIPHCR0eDzFHkRRzjTb/8PeXy7zxxGQDAsgfHdhJR99rX/AD/cuRC\n6TgxesenZvk5XnyFZl6jRGlFZYsSNhKUdvJ07/E7Zvw0hyKnXDUfNZ99qR8B11xzDT784Q/jvPPO\ncyI6hmE4vwTYjSdtKZW4sCwL7XYbjUaEnhAxIgpv27Yd4R30F3mv14NpmpiZmZnCFifL8vIyGo3G\nVD0WxXml4rkkE3A8TMyJ0bkjZ17ueswEHYMXdf+4vNNzHf+1fK7z/z3rf4z/++/e4Tme5/EP3Oze\nDi5K1Ov1pp6aNQwD3W4Xa9eujXU9aeDMmTNYu3ZtoH6xbB4X+5emDghBsSwLCwsLaDabSW/KVBDP\nJdu2Ua1WUavVXNf3arWaieMXAOVOUITOB9u2US6Xce+99+Jb3/oW3vKWt+CDH/yg8wugXq/n5UsS\nmCykXFV9bce1FcnCPkdFnKbZ46ZSVezc9Qw2zy6OPP/wT3dgTWW0Ol0kaKSOF3MA8OjCyxUj5QRJ\nzfJeXUzcUWp2csJ8l/081LJwXIo2h0yM3p0+fRqapknnS+YditBJOHPmDB5++GEcOnQIhw4dQrvd\nxlvf+lZceeWVeP3rX481a9bANE10u13Mzs4mvblTx7ZttFotrFmzJulNcWBROCYU+JRdqVSaOHXC\nbrj1ej2iLU4vrVYL9Xo9knRT2OPiJ+L4ANuFFz2Dvq1ja2PgE/ncyjrXWFHQidE5nt1zT3uuVxR0\nQPgonQoxescyAL1eD/1+3xEQUaZmixShO336NNavXz/RZ8d3QGCVs3yaL0j0b1qwqt7169cnvSlT\nhwm6ZrPpTJNh2ZUcRSyVF7LMCLpDhw7htttug2VZuO6667B3796RMbfccgseeughNBoN7Nu3D7t2\n7XJesywLl1xyCbZs2YKvfOUrnuu66KKLcO655+Jtb3sb3va2t+HgwYNoNpv4jd/4DWeMaZrodDqZ\nSTtGzbTScl7wtiKmaQKAIxSiTo+QoAuOLJWqOi5hBBzPBa8+BgCOmAPGF3Qr/cHE69ef9YRyO1SC\nDkAkoo6XZSIvAAAgAElEQVQRJDUbhXVOt9tFr9dL1Y+yuDh16pRzg48KPnpnGIYziT8Ntiis2GPd\nunX+g3MGE3QbNmxwPc+qnnNCtlOulmXh5ptvxuHDh3Huuedi9+7duOKKK7Bjxw5nzEMPPYSnnnoK\nTzzxBB599FHcdNNNOHLkiPP6pz/9aVx44YVYXBxNz4j8x3/8h+tmtnHjRpw6dco1pkgh7bSgivYw\nt/E4JzAXKeU6DnxBg1+hyav3DUScJvk4PYJoAICzzv8ZNsyuABiKuR8tvARrK13XuCDpVpFHXtwu\nFXUyMQcM0q5M1EUFpWajJa5zlrdFmZ2ddebetdttmKaZaMFL0VKuPEVu+wVkRNAdPXoU27dvx7Zt\n2wAAV199NQ4cOOASdAcOHMA111wDANizZw8WFhZw8uRJbNq0CcePH8fBgwfxB3/wB/jTP/1T3/WJ\nX4hms4kf/9h94S76DT7OeVY8sigcE3BZmaScR7xSqWyeIg8Tca5laJD/1uRPK+71s14xFHPAQMhN\nCovOMVSiTsV3lrbhTb/8PfzDv75q4m2Roaqa5UUE64zAV2emKQWYBuK8TmialipblCLfl4rc9gvI\niKA7ceIEtm7d6jzesmULjh496jlmfn4eJ06cwKZNm/ChD30In/zkJ7GwsDDW+pvN5sh7s+CoHydx\nClpVWzRmI5BU0+miXChV+6pKpcrEtUzAAYAt+fHMInW2PrrO+uYW1swMom+8mGtzQkyMzsnwmj/n\nhSo6x+hZJVR0E2/65e/h8L+9Shp1jApR3PET+FUign74TJ802KIU9XgX9X7MyISgm4QHH3wQmzZt\nwq5du/BP//RPY92UN2zYgDNnzow8P60oVd7JU1u0vBHGs08ahSsJ5xsTVtzzrhGrz9fPGoi3NTNd\ntLpV1Gs9AMCLKw00qt7p1HHSrTxho3Q/WdqAl609hTf/0kDU8cQl8IKmZvkemSw9W6TrVtL7KTPI\nNQzDMchlJubTaE5fBChClwHm5+fx7LPPOo+PHz+O+fn5kTHHjh0bGfOFL3wBX/nKV3Dw4EG0220s\nLS3hmmuuwWc/+9nA6282m1JBV2QmjVjJhAIZMicPM/jt9XrodrtO2b9KXAcSca7s3+prVc6kuWyh\nVB2k06vVgaDXVpWQKOaiREy38nzlv1+FV6z7me8yjre8Kwn5wOA0o3eyHpl8ahYoxk0ubeJG13XM\nzMy42luxTiJRzYlM2z5PkyLvO5CRKlfTNPHKV74Shw8fxubNm/GLv/iLuP/++7Fz59AI9ODBg7j7\n7rvx4IMP4siRI7jttttcRREA8Mgjj+BTn/qUb5WriGEYeNvb3oYvf/nLrudXVlZQq9UKOV+l3W47\nc0KCIJr7MqHA0kZpn8iaRquWqBDnKTLjZVnUIJCAKwuPK+LrQzHHhJzGqR0m6gA4Yo4hRueCFEP4\nVbeKLBhD82gvUSeKuZetHRROiVE6GXGKOx6xapaJdTZ5n48QJV2dGQemaWJpaWmky08a4ZvTi7Yo\nYX7krqysQNO0QlTki7TbbViWNeI+we41OSHbVa6lUgl33XUXLr30Use2ZOfOnbjnnnugaRpuvPFG\nXHbZZTh48CDOP/98NBoN3HfffZGtv1qtwjBGbxRFmlclEmTfxUb3rKsGzetJHlUqtVqtot1uO8cI\niEfEWf2BgLf6OkoV03mNF3MifqnWMHhF53ieWtwYKFIHAMdac9jaOIMLXn0MP/rPrZ5jRY05zdRs\ntVp1flRVq9WR+V18ajbrZCliozI1brfbrtSt37FRtb4qAkXedyAjEbo08NrXvhYHDx50PdfpdJxf\nuEVDtu9xm/smCYvQJe29Ny6yY8OOixiZabfb2PP//fXoMjxTqatjyu5+t5og9DRe2HFCDhgVc2Gj\nc0DwCF2Q6ByPKOpUqdayPty/H31PIep8rqqiuJMFGKMQgN9+77UuY3RZ26s0GueGIQ8muyyCzo4L\nb4siOzYsrV6r1RLa4uRotVqOKObJel9egWxH6NKAaqJl0SN0KnPfvEXhsrgfYY6NsipVFHHAiJAT\nRRzgLeQAtZjrtAfmn825luv1VruGVnt4gyqVLPwM7rRKSR/dDgB45cafSp8fF695c31Ld0TdBa86\nhh/+1xZolhiOE94UQMCJRDE37+K/vtf1mFXO8hEiwzASsd6IiixF6FSEtUXJwz6PS5H3HSBBFxjW\nRiRHKn9sLMty/hmG4TL31TSt0CdU0nilUoN4wwGCtQhTDrylCNNNq2JPM4fHmwlAuz94jgk7u88t\nVLfR7w4vPXrZcoQcAJTKFhaXh/N/SiW5UONRiTkA+OHPBn51TNiFjc4Bw9Tr917cjGZ9RTlO5JU/\ndxw//K8truc8Bd4Y4iyqwguxsIIZ57IfBqwyc1rWG4QcP1sUNqZcLhfu2JCgIwKxfv16LCwsuPrB\nFSVCJ7MV0TTNqdgqygmURrsHVbFJmKpUQO4PB8At5BiSqJ0skidG6WTL0sXInfhYIuaCCDwZTNht\nXR++Yn3FqOJ7L24GAJxuzypF3ZnOQIjqq8psw+wKXvlzx3FqZRY//cmgHRHvtxeVuIt6Dp4o7th3\nCnBP3m+1WqlOzabtfI0amS3K4uIiTNPEwsICdF13HZs8fxYA2ZaQoAvI3Nwczpw5MyLo2C+ivOHn\nP8aeL8qJkiZUqVTWoUHslapM4SkiOy6DX5sbO66QA8YSczKkAs8jOidiWjqePj0QVuc1T/mMViMT\ndUzMAYAFDTpsnFoZzlF7yctO4afHVq8fqxHMwOIOSGxGs6ywwmvyPhMQaUjN5l3QibDzf3Z2FqVS\nacQWJW9FLyKWZeVyv4JCgi4gMnPhPEXovCI9slZOxHQRBbZXD1ux4b1LrHlc62SdGgAAbPG84NBH\n062DZQAjykNYrijkALmYGzcSF5SnT29wRJ1XunXFkDf15kUdL+YYTNTxNDa10DrZcFcFS8QdEC56\nN62qWUCdmmXtyCg1myxMxIrRO9GPUOw3mwchpKpyzcO+BYEEXUBU3SKyLOh4W5F+v++Y+8oiPSJ5\nErNBmeY+h02liiLOtSzVYbThjtJZgrCQ3X8Voo9P2do93T2WE31ayYZlCGk5zYbVGy6gUu8HTrWG\njc6JPH16A0xTx1nrlqXvUYk5hkzI8YiibrZqAJsGf396cj1g6FJxB0yWmk3K0JhPzfJdEVhqlm9H\nNg2KFqED1PusskVZWloCgMC2KGlGtu9Z3ZdxIEEXEFm3iKx9UbxsRWSRniDLI6JDTKUy3z5VKtVz\nWX5fTcXrtsa92RRerIyKpzBz7zRZxaxEbfS7JfTFUloNmF3jtimZVMzxvLi4RinqVLS7w+KK2Rm1\nR55M1K0YVTSabfT6JRiLq9W7ORJ3wEDg8V0RmIBYXFxMXWo2TwQRsezz54texG4iKluUtEL3IxJ0\ngdmwYQN+9jO3F1UWolRx2YoU9QIc9fHmo3BhU6nKbQxyaPi5cX7vkUTa2Hs1C7B5EaKI4AUVc5rs\n/aurXVke2paI4m5cTHP4Gb+4OOgCwoSdX3SOZ6VTVYq6lc7octbMdLFiVFEpmzBnB357VkWH3Vu9\neRq62x6GE9dScRfwazktcQf4p2an0bC+aBG6ca5PYW1R0vp58qlmnrRubxyQoAtIs9nEU0895Xou\nrYLOSyREZSuS1n2Pk6gaZ8tSqZVKJXQqVbmdAefMeb5HNZ8OGInuaSySpNvueXYAUFNE0UKKOZF2\nyy2S1qztYHlpBmvWdkbGqqJzvJjjeXFxjfPa2sbo8gB3dI4hE3UyMQcAy52BOO33S9B1G9VqHx1U\nYFo6NN0CX2ul9QVxx0fu2H9XxXUYkpx3JwoIVWp20rldRbtGqURNGERblKzMiyyaeJdBgi4gspQr\nI+kvksxWhHVxKJKtSFqJMpUaaH1jpltd7xWFmW6r36cSfxoGkSaRmpjLVYg5BZpEeSwvzbj+yoRd\nUHiht9QaLI8XdjIxx2CiTiXkRMplE/1+CYZRhq7bsEoW9LIFe1WE2obuMm7W+l5p2eHTYcUdkL7U\nLD+3q1qtjh0dKtL1L2oBy0fvADjROybw0mSLQj6xJOgCk7Y5dH62InFvW1EjdEH3OY5UamTwuxAk\n5QqMCryS7S3kZKtlz0uKImwAuij0JMuRiTkZTNjZtiZNz6qicyqWWjNY2+h4ijnGwlIdlcqoaFXB\nRB0AlKuD91msAITThbahOzYxTlSUT2WbcnEHTBa9Syo1y8/tGjc6VMTennFe+1WmxqItShKmxkX3\noANI0AVGFaGbltls2KrHaZF0dDItiMfHtm3PKGmcIi5UytV2v0dZ5CBiYVTkldVRPLUX3nBjrS4n\n9FgWlxN5QcWcs87VlbK5d0zYeYk5r9eCiLne6hy4Xq8UWtQBcAm7vlGCtirs7J4+bJ/W04GS7Xym\nrpQ3Qzg2k0TvkhR3srldLDrEzq882W5MyjSvx7wtCj8vstvtJmKLQvciEnSB8RN0cTCJrUjcFP3E\nAdypVL/jM80oXNB5czI0Cy5RNrIs1R1dw2jRBGv7FUDMuZbDwUSepmE1itdXLMyNLVmpU1TBrba2\nWpAA+Ai9vg6Ta19Wm+mNjGFijn8sE3WG4X3ZtVc/RyZgrX4JWmUo7Fi1scasXliUjku/eom7SVqN\nJTXvDhgIPD46FCQ1W7SbfJL7m7QtCkXoSNAFplqtotcbvYhHKeiithWJmzS2wooT1hnEMAxXKlV1\nfKaeSp0ExSEUb9ijAs9jmUyY8O8v296iUPY097zF94BViDuZmBu+6H7YXRlE3cqSeX0MXsg57+tU\nHFEnCjkeXtT5CTmGVrIdUQcAetmEtRq5Y96Adk8bmjuz7eM3k98d7vOOso9s3NE6kTCpWXZOFm1a\nSFqux0nYoqRl35OEBF0IVOp/kotGXLYiRDTwqVQm6KOuSo0aXxEmQ7AxUS6bEwS2JlmZzzIG6UFu\nGczbLoCYE+HFHTAQeGHEHE+vPVhWpR4sAggMRJ0eoJtFZ6Uq7Y7hBbN5YcJOX03JMmGnVVZf72mj\nRRNAOMsT5wnu/z6XtGmLOZGgqdler+dMUUnDxP24SaOomZYtiqooIm2fR5yQoAtBVF+MadiKTIO8\nFkaoUt2s0mtmZtgmKg0Czo9x5tQN3ih5WXxOViwRAq2nu1O8nHlx2NPA6pbBvo4jBRYem2Vz+9Br\nl12iThadc95najDNgXIqVeURPnM1emetLieIsOO7Zojb5+zIanpYY0PFeXR8+ttp3SZsv5+48/rM\npjivzg+v1OzCwgIqlQosy8Ly8sBfMA8dEVSkUdCJxGWLUsQCGBESdCFgKTf+SxNE1JCtSPqRiWwx\nlWoYBmzbzoSIExlrXh0vBINeJ8V5dF4CT1bFyouZavColngKsrl3es0MLOYYLFqnSzpjOO8T9tM0\nSiOizpSkYq2+PiLqRAEnoun26HaWLEfUARhamYjVrzJhB4yKO1ZgkWK7k6DwAu/R37zGEQdi6o95\n3jHbjTyIgaz9wA5ii8K3i/O6V2ZBzMYNCboQrF+/HgsLC2g2m85zKkGXtK3INMhyhC6syM6iiGNM\nUiTBEG/0Ywk8XtwF2SbRw04h8Ly+glZnKKrEqJ1MzA1f1Jyes7og1EQxxzCZHYvPvjFR5yfkeJhP\nn2ubWbo3iLDjnxO3kU+jZ8TLLih77v+s839VapbNvUuTp9q4ZF3UTGKLQkURJOhCMTc3h9OnT48I\nOsuyUmsrQgyRpVJVIjvLAk5knM4RvsscR+ApqmADY4xG7zx/T3hE7fzEnOt9nLBTiTnnrSwV6pFa\ntU3dqajVQvSjZcseSXM7r48KNi1A6tVJ064u1/m+TFAwAaRP3PlVzfb7fRiGkfnUbJa21YugtihM\ngGddzEYBCboQiNYlfJSn1WqlylZkGqQ9QmfbtnOhDlI1nCcRpyIOcQe4BV7g6B2LGGm2exJ/EFbF\nnQb3vLvhRijeZ2uwOsPLnsZH33w+EPY+TeEvZ3ORMrsvF3a2Kc6P05Wiji1jJOInCDCGWEgBYGhE\nLBN2NtziThvazERVDZsGIadCLKzgU7Osmj1rqdk8zyNT2aIwAc4CKmJ0Ne/3YR7N54ac4tNx+nz0\nox/F2WefjWPHjmHr1q248soroes6bNtGvV7P7YmkotvtOuXpaUGVSi2Xy9I0ShFEXBCiFHeu5Xqd\nEqq7/QQuBrZX0YHHTmoe8+UASKNivLAThdroYO+XgWG0zpYVYni9XzQRZnYxsl1SRSY9dl/ziUp6\nkWZBp+LxD9zsesynZnu9XqpTs8wSpFarJb0pU4Nd8xcXF1Eul9Hv9x1xXq1WUa/Xk97EqFF+4ShC\n58PS0hIefvhhPPjgg/jCF76AZrOJSy+9FG9+85vRaDRgWRa63W7hxFyaKGoqNUrGsjoJslxZatbv\nLi8GwEIIPI0TQy5x5yXmbAzTueI8PY/UrN0rqduf8eOYwPJKMZsabLOk/mwkaVCbnxMn2T9bl4g6\nRXQPOoaiTlgWE+V5mFMXhDCpWdu2HXGXhtRsEdOOrDc2AKxdu9Z1jAzDyKOgU5K5CN2hQ4dw2223\nwbIsXHfdddi7d+/ImFtuuQUPPfQQGo0G9u3bh127duH48eO45pprcPLkSei6jhtuuAG33HKL57pu\nuukmfO5zn8Mv/dIv4e1vf7tT/Xjttdc6YyzLQrvdRqPRiHxf0w6r+pz2r0GvVGqpVCpkKjVOYove\nhbQ4ATBW9M5rPZ4iw2eOny0IHFGwqebbucapol+KDfObw6c6WI4YkwlUlVCTLMvZrAnvDFkRdyJi\n9I5ZbvR6vZHIUBI/8hcXF1Gv11Gp+LepyxOWZY0ULAJwqmRzhvIikClBZ1kWLrjgAhw+fBjnnnsu\ndu/ejf3792PHjh3OmIceegh33XUXHnzwQTz66KO49dZbceTIETz//PN4/vnnsWvXLiwvL+Piiy/G\ngQMHXO8V+cEPfoCXvvSlWLNmjbPso0eP4nd/93edMbZto9VqOWOKxDQFnSyVygQcpVKnR6bEnWSR\n9qqY8hUU/OuV0cGimGMwseYrvBDQZ0+zAy1rBFtTR9SCpl25g+35eZG4AyBPzQa13IiKhYUFNBoN\nxwakKJimiaWlJczNzbmeL5qgy9RRP3r0KLZv345t27YBAK6++uoRUXbgwAFcc801AIA9e/ZgYWEB\nJ0+exDnnnINzzjkHALBmzRrs3LkTJ06c8BR0F154oetxs9nEwsKCdGxRQ92WNUYeJiB8FM7P+oUE\n3HSIrahCMpHfE1sD+KYOfNTLy/qurw1fl0XgZO/trW5bxVYKOQeWuvXah1VBZWNYyCBjIOS0wIon\n8Fw3WdqV3y9Z+parXxk+GWx1fkyzP2yUBEnN8pYb00jNprlILU6KeP+VkSlBd+LECWzdutV5vGXL\nFhw9etRzzPz8PE6cOIFNmzY5zz399NN47LHHsGfPnlDrF6tcgWJV0IhEXeXq1cuWVQ7zkIhLltjm\n3QnCxCXwVCuR+a6JiC+x9zBh5/dVNvRBVa2i8IKvDGX74Np2SWTMmV/HjRuJyEnVlHs9oRC3Q9wd\nhWqPS2hlRcD5oaqa5S034uxlyijiPYk86AZkStBFwfLyMt75znfi05/+dOg0qUzQAUNhU7QvTxSo\nUqmqNAWJuPQyleid37QkVacKL9HAFxfIBKGwM6zwggm7EYsPfiwTdn5T38xBitRz/2yP6lUvvDz3\nALU/nZ+Ym9Cnjl9NXkQdQxR3vOWGqpdpFKnZot6HVH1ci0amBN38/DyeffZZ5/Hx48cxPz8/MubY\nsWPSMf1+H+985zvx3ve+F1dccUXo9fsJuqIx7n6H6aJBAi6bpMbvjgm8ANWorvEl23fDXW3KVJFB\nZta7+lCWTub3if1f3DdpJE6lgvwEnPQ9wmOx0lVWrRrhJS+L1bBBCZuaZeIubGqWFYsVUdBRhG5A\npgTd7t278eSTT+KZZ57B5s2bsX//ftx///2uMZdffjnuvvtuXHXVVThy5Ajm5uacdOu1116LCy+8\nELfeeutY669UKuj1eiPPF1XQBcUrlZq3NlvEKKkQd7zICSLuXFE7yeviInghKK6PwyXMPJSLprAQ\ncW+DkIoNI+T8onxsmV5ROg2RiLq8CTg/4k7NFk3EAMWNTIpkStCVSiXcdddduPTSSx3bkp07d+Ke\ne+6Bpmm48cYbcdlll+HgwYM4//zzHdsSAPjmN7+Jz33uc3jVq16FX/iFX4CmafjEJz6BX/u1X0t2\npzKMl5ClVCohI2lxp9lwpWVHImayrzPzxSspXudhBRRe915nWz3m/Xl1ahhZluY9ZmS9AQlygJzQ\nY8hlS1ZTNGEHeKdmWTcEwzACpWaLLGooQjcgU7YlaeB1r3sdHnzwQddznU7HaexeJEQPPlUqtVwu\nQ9M0SqUSSuLuVOEnFmy/qJ24gaII8xJLpQBj2DL9omxagOXwiwgj4gIehDhSrtLlFxzeFoVPzfZ6\nPViWNZKaVVl3FIFWq+UIYZ60t2obk3zYlqQBXdcdg2FGkVOutm3DMAwnlcoEHKVSiTBMpVOFxzLF\nwgZH4Kk2xAwRVmLpWy/RaPPjFGNGqlEDjvMixAdNKdfpokrNAhhJzbLrblFh956iQ59ASObm5rCw\nsIANGzY4zxVJ0LFUKovCAYOTiVKpRJTEkprlT1G/QBirTlWIq2GUiq/A9VGlsnl8sssGL8h0qAWa\n2A4s6CVoEhE3MiDkuiUUOeUalCCp2U6n43RMYOKPZUfyjm3b0khcEfadhwRdSObm5nDmzBmXoMs7\nqlRqtVrFysoKarWac+KQgCOiZqriThAV4tw8L9HBonyBpp45gtEraqcN5+8pe7xqnLDzWVZAQgmr\nGCpdSdh5I6uarVar0DQNKysraDQaMAwDKysr0tRsHiny/EEeEnQhUZkLx9kxYdqwqlQm4LxSqZqm\nYde+v0hwa4kiEbu481p30PStYhtlQoVP9dq6h1WKqHZk48SVxSHiYhBbJOAmgxd4R9/9Plf6laVm\nu92uk5pl4i5qQ+MkoaKIASToQrJhwwapoMt6ylWWSuU7NFAqlUgbcVXMBkJMdyrQ7BBjfSJ8g2Vx\nAjDAOK/PJalI3Miic+xBN21+8W8/4/xflZplhsaapjniLuupWZmgy/L+jAsJupCoInRZFHRiKpWd\n/NVqldpsEZkiMXEnKxRQvRZwDp+4LyqRwwfr/Mb4jRshoctZHrtGJIUqNVutVh3POzE1y/5lqTK0\nyIbKIiToQrJhwwa88MILrueyIujCpFIBEnFENklF5C7MONk2rr6u+UX3bEEATbispCARFz9iYQWf\nmrUsC4ZhwDAMtFotlMtll+ddmmH3XorQkaALTbPZxI9+9KOkNyMwlEolioyfuJMJiUTTtyphE2Vk\nLQXiiQRcsojiTtd1zMzMjKRmFxcXU5+aVVW4FhESdCFpNptYWFhwPccidGkJ+1IqlSBGCSoiUpO+\nJYgpkPXUbFruu2mABF1IVEURSaJKpVYqFUqlpg3PmewhxhBTIdH0bY6hQoj0krXULFW4DiFBFxJZ\nUQQwjNJN60skplI1TUOpVKJU6jQJelcKogTCjgm6Pi//siDLIhwykb7NEPS1Sz9hU7NM3E0zNUsR\nuiEk6ELCOkWITKMwgo/CUSo1Ifx8wpLYDi/PsSiFIuEQdfo265FAL3s82TgiewRJzfZ6vamnZilC\nN4QEXUgqlQr6/f5U1iWmUm3bRqlUolRqVARNbab9Dhvl9onLolRwZMg+SqnZcEbEXdBtp69HPlGl\nZuv1OizLQq/Xc+besfsWCz5EKbYsy0rFXL40QIIuIqKK0PGp1H6/D13XKZUaJVGlP4sCRfhiIYoI\nX5BsumpclMtSQV+F4iBLzdZqNdRqNVdqdmlpCQAiTc1ShG4ICboxUH15xhV0qlTq7OwspVInhcTZ\ndCFxFxvjiMBpLIsgeLxSsyxgwadm+XZk40TayLZkCAm6MdB13RFejDCCjlKpMUMiLh14iTtK3xJE\nIRgnNct6zQaJslFRxBASdGOwfv16nDlzBhs3bnQ97yXobNt2BBylUmOARFy6CXp8KMJHELklaGp2\neXkZQLDULKVch5CgG4O5ubkRQSeL0MlSqSy8TKnUCCARl29I3BFEbgmamm232zBNU5matSyrkOJN\nBgm6MVCZCzPhxgoaAFAqNU6CeiUQ2YfStwSRa8KkZnVdd8Sdqsq1iCKPBN0Y8IKOtdnq9XqwLAvd\nbhelUgkzMzOUSp0WXj5sRP6g9C1B5Bq/1Gy/34dhGFheXoZt22i3247A0zStkGIOADSfifx0FZTw\nR3/0Rzh58iS++93v4ud//ufxsY99DLquo9/vo9FouMaSgIsJEnDEuJC4I4jM8vgHbnb+b1kWzpw5\ng3q9jl6v56Rma7Ua1q5dm+BWxory5kcRugD0ej184xvfwNe+9jV89atfxYsvvohf+ZVfwe/8zu/g\njW98I+r1upNu5SExFzEk4ogooMgdQeQCFomr1+uu1KxlWQlvWTJk1rzl0KFD2LFjBy644ALceeed\n0jG33HILtm/fjl27duGxxx4L9V6e66+/HrfffjvWr1+P/fv343Of+xwuvvhivOMd73AicrKiiO++\n/0bnHzEhJOaIOLC14b+gYwmCmDqPf+BmV3QOGK1wZanZ2dnZaW9eKshkhM6yLNx88804fPgwzj33\nXOzevRtXXHEFduzY4Yx56KGH8NRTT+GJJ57Ao48+iptuuglHjhwJ9F6Rv/qrv0K5PPyoHn300ZF+\nrn4+dLyoo8jdGGSlHxKRXWRtEWTfNYrwEcRUEAWcCLX9cpNJQXf06FFs374d27ZtAwBcffXVOHDg\ngEuUHThwANdccw0AYM+ePVhYWMDJkyfxk5/8xPe9IryYA4BmszlS5coIYnJI4m5MSMgR04TanhHE\n1PETcTzkQecmk4LuxIkT2Lp1q/N4y5YtOHr0qO+YEydOBHqvH81mE6dPn3Y9x75AYV2rSdwFhMQc\nka2YgakAACAASURBVHYmaXxKEAUmjIjjoS4RbjIp6MZh3D6rMubm5kZSrsDkvwpI3HlAnnNE1qDo\nHUEoGVfE8VCEzk0mBd38/DyeffZZ5/Hx48cxPz8/MubYsWMjYwzD8H2vH5VKxTEO5gnTz9UPJu5I\n2HGQmHPDf9W8Pho7wJig46JcZ9Bl5QE/cUfRPaIARCHieChC5yaTgm737t148skn8cwzz2Dz5s3Y\nv38/7r//fteYyy+/HHfffTeuuuoqHDlyBHNzc9i0aRPOOuss3/cGQfWrIMpIIEBROwAk5HhUXy9R\nHMnGyQRUkHFRrjPosvJM2Ll5AAk8IrNELeJ4KELnJpOCrlQq4a677sKll14Ky7Jw3XXXYefOnbjn\nnnugaRpuvPFGXHbZZTh48CDOP/98NBoN3HfffZ7vDcu0BB1PYcVd0Stcw36lgowPuswox42zrAIe\nbimUviUyRJwijseyLJRKpamsKwtQp4gxeeMb34gvfelLri9Tp9NxerdOk8KIuyKJOTrzRokiZZw3\nSNwRKWFaIo5neXkZlUoFtVrN9XylUsmznQl1ioiaubk5nDlzBhs3bnSeiztCpyLXkbuiiLgk78uq\ndWshx4QZNw7jpozzDDs/SNgRCZCEiOOhlKsbEnRjwrzo0iDoeHIn7oqSbvUSKHEQVYo06jTqOOOi\nWG/WoTl3xBRJWsgxqCjCDQm6MWEROh5N01LVQy534q4IBImKjUta7vFJFUqEWV7W07c0546ImLSI\nOB6K0LkhQTcmGzZskAq6pCN0KjIp7vIckZMRx1cn4DKDBkLDjvMd4zPOWR8bJ5sWM06aVyXuxGXl\nIcJH4o4YkzSKOB7LskbEW1HFHECCbmxk3SKyQmbEXRHSrQlG4VT3dvFj9xvnNY0r7LJ8x1nucZ5Q\n+nYUSs0SPqRdxPHYtp3n4ofQkKAbk40bN+K5555zPZfmCB2PbdswTRP9fh/f/J/vhq7rKJfL2P25\nfUlvmhpVo/QskkIRp1qmM1710dvCMoOM8xgzso0RRAv5ZfstMzB5EHdA8OgdRflyzb//1vvR6/UA\nAK1WC9VqFeVyOdXRLtW9Ns3bHDck6Mak2Wzi8ccfdz2XZkFnWZYj4kzTRKlUQrlcRrVadX7hpC5y\nlxcBJxLFPLkYRZzva0HmvUVhXCxbngJX+tbjB3ugcbLtKULHC1G0qc4/Ene5QIzEsR/6vV4PKysr\nsCwLlUrF+Ze2SBibP1dkASdCgm5Mms3mSD/XNAk627ZdIs6yLJTLZVQqFczMzPieBKkQd0VIuYZh\n2iJONdZHZLnSol7iKsg4cZ0AII4V9kG2XGk6OO70bZa/skHPNxJ3mcIrnappGsrlMsrlMur1OizL\ngmEYMAwDrVbLCQBUKpVUmPlShesoJOjGhNmWyEjqi8Z+YTERB8A5CUul0tjbROIuQsYRUAEIdS+N\naqwg7DRJgbcormRjZOM818vGBhBhmrn6f5/gQizp27yIu6CQuEsl486J03UdMzMzmJmZgW3b6PV6\nMAwD7XYbuq6jUqlMfG+ZBKpwHYUE3ZjIBF1SX2qWRu33+858uJmZGei6Hvk2kbibkDDpVr90JBsW\npV8c5KJLWYVqBZ+D5Ygr1bjVlbBxtq6YIyOJ2rkifLK38fsUVNzZ3hHGkXWRuBtC4i5Roi5s0DQN\n1WoV1WrVuef0ej0sLy/Dtm0nclepVKZ2H5RVuBYdEnRjMjc3N5JyBYZp1zi/aJZlOSJONR9uGjBx\nZ9s2du37i6mtd7DSHJzIQQRbAAGorDKdUMS5XherUC3J5y+7icuOk7jBimPJr8PWbU9doFmD5ahE\noAsvcRcgfatk3KraHHyVlZCYmxrTqk7VNM0Rb7OzszBNE4ZhoNPpjKRm47wfqSpciyzySNCNSblc\nhmmaI8/HMY+OzYdjIi7sfLhp8M3/+W40Gg1omhZv5C4PQi6u9GjI9/mJuBFWBZZzBDzn0A1e9JxD\nZ/qPYctj4s4uSXaM+06IItCXoOlbxCTuwo7NCiTkpsLjH7gZ/X4frVYrsW0olUqo1+vOvDuWmo17\n3h3NoRuFBN0EyIRbVIKOtxZhwrFcLqNWq8WSSp0EcVtiTctmOd3KCJhKnSjdKqsyFcZ6+b05yCJx\n4vICzKHjBZA4TiWUpMszOWHnc/w1S4NmAVZZvZO+6VvlskOM5yxbIhWCaYZSrrEhq05Ny/1A13XU\najXUajVn3l2v14tl3h3NoRuFBN0ERP3FYXMTmIhj8+GmnUodB1WqmcSdgiBz6SZJt44MDPj+EeNZ\n7/e7RJeXZ1zAaKBmDebQ2T4/5vXecGWW5CrGr0/v82OHO+JnXhxUfGlcoF7cbnEdY0X5MvbVHoHE\n3cR4pVPTJOh4+Hl3s7Ozkc+7S+t+JwkJugkolUro9/sol4cfY9gInWo+HIvE5QkSd6vEkHJ1CTM/\nH7URkREk3+h+r1SgKQSINjozQSrY+HFOYYQokCTr1QcF3Y6w8xKPel8bFDt4RO3E4ozhNrMwm/qt\nrvcESCU7y/Yam6c5dyTuAhN0TlwWhE0c8+6oS8QoJOgmgHnRbdy40XnOT9CJ8+Fs20apVErVfLhx\nCCtkIxV3aRdwInGnXH2ias6wIEKOjZWIMiVeok9Ynl3yXvawMtZ/tbqxukzVVY37PDQuaueIO78U\nbt9jHp8Mtv8hUrhB0r2Uls0v4xQ2ZEHQiajm3a2srDj3Q5aaVcGMj0Wy9llECQm6CWD9XP0EXZbm\nwyUBE3ep6E4xLaaRcuWFo6yWYLVoQCXsHEEWplpWFGc+adggQsYVyZJd38U5easRO5ew84qq9TVo\ntjx1K3s/m8c32J4Jq2rFbRH2pZBz7oBCCbxJq1PTYmY/Lqp5d4uLi07atlKpjLQiy6KQjRsSdBMw\nNzcn9aKzLCvT8+HGIYpikLGjdllKt8oIElHzGeMIO1VUzOP9TNjxc83CrNszeidJw6qKJ0TxIi+K\nWF0sE3ZeUcA+fIUa/9VhqVuAe49flDNGcQfEWFmbdnIevYvSYiRPwkacd8dSs3wrMibwqChiFBJ0\nE7BhwwaXoONTqf1+35kPl+VUalIUUtyN4Us3cq/zi+qtrkMWlXPaZHmJQkkhQCDs1eVGUDgBDNOr\nQcSaOMdOfN1z+aMZHfX6SNzFQ07EXZw+cXm8v/CtyAA4fWY7nQ6Wl5cBAL1eD7quO0GSPH4OYdB8\noirZPXumwF133YWlpSU899xzOOecc3DttddC13XYto16vV6oL1en03HmPsTJ2GnZNIu7CYsk/K1H\nvF/2S7lKhVaIqlX5C5Kn+u7HqrlwMjHJizW/z8Ovgla1b0HEnWzdXrYpSkIG8QPNvWOk+FQIRQbE\n3TTMflutFkqlEmZmZmJfV1qwLAtnzpxBpVJxgicsejc7O5v05sWN8gymCF1IVlZW8PDDD+PAgQP4\n4he/iJe85CX49V//dbzuda/D7OwsLMtCt9stlJgDokm5BuG7778RlmXBNE1c8jf3BX9jmiN3AYsY\nVNg+6Uy/qJ1vylUGExABerNKsd3bJYo5/jkm7Lyignp/IOr87vGa6V6OVRUGeGx3yRj+3xTfB/W6\n2ecaSthR9M6flEbuvvWe/+WIi2mQp5RrUNj+rlmzBgDQ7/edqtkCCDoluYrQnT59GldddRWeeeYZ\nnHfeeXjggQewfv36kXGHDh3CbbfdBsuycN1112Hv3r0AgNtvvx1f/epXUavV8IpXvAL33Xcf1q1b\n57zvjjvuwCc+8QlccskluPzyyzE3N4ef/OQn+P3f/31njGVZaLfbaDQa8e9wimAiNq6LGEtn9/t9\np1NGuVx2DCpzF7mLoArWu8pUvd+q93kuTyLIghIofRukynV1G8xa+PV4FkRArRfM6vhagiJ3EZES\nMff4B26GZVkwDMOZ2M+sOuKcO720tIRarTY1AZkGLMvCwsICms2m63lmXpxzlGdqrgTd3r17sXHj\nRtx+++248847cfr0adxxxx2uMZZl4YILLsDhw4dx7rnnYvfu3di/fz927NiBhx9+GG9605ug6zo+\n8pGPQNM0/Mmf/Inz3h//+MeYm5vDhg0bAABHjx7F3/7t3+KP//iPXctfWVlxfjkUBcMwYNs2ajXF\n3TQkvL1Lvz+4U7M5iX4u44UTd14VnDa8Cwc8rEtUHR2Uwijg1ULvSd6quNfpglCUpT3FMQxe2Hla\no3D7GSbyJhJmvt3IeyMWd9Kvcpivd0pPBYcUiTgVtm27xF1QO46wLC4uol6vF0HIOJimiaWlJczN\nzbmeL7qgy1XK9cCBA3jkkUcAAO973/vwhje8YUTQHT16FNu3b8e2bdsAAFdffTUOHDiAHTt24C1v\neYsz7jWveQ2++MUvut778pe/3PWY2ZbwMKFRxDD4pDB7F1ZUAsApKglj75Krgoog9y2/lCt/4x+x\nxeA6JwhRO/YR6CMGu2y8YjuUqUf1azL7EplQ03tu4aQScwBQ6gaIvAmfB0urMmEXRjfwQjWsuFN1\ns/BEkpb1/NqGSbWmPS2boM1J0HlxmqYp7TiibINVxHsNVbjKyZWge+GFF7Bp0yYAwDnnnIMXXnhh\nZMyJEyewdetW5/GWLVtw9OjRkXH33nsvrr76as/1iVWuQHG/UMyuJSy8R1+/33fsXer1eiQpikyK\nuwmKJHynFbFKVlnEiok7IWpnrQq4sMJOFonzq+TlvelUOMv1OSxaHyhxgs8U5ox7rafc4d43RtB5\n6uKOVR8zj+Qw8+gA788y7eJuCkxa3ODVBguAI+5Er7UgZN2HbhyKKGKDkDlB99a3vhUnT550HrMD\n+7GPfWxk7LgH/OMf/zgqlQre/e53e46bm5vDwsKCdL1F+8KFKYoQPfpYKjVuj76Jxd20hF0Q02F+\n7Bimw3yl54ggkwg7zeIidoqo2EirLN2jSEOyTTpXdKDs9iCMtVTz5STbWOoMRZ3nfEAxatcd/B1H\n2AGTizv2uUutUFTWgWE6TwDBRVua2pDFHJWLq0KVb4PFOiWovNaC3kOKdK8BKEKnInOC7utf/7ry\ntU2bNuHkyZPYtGkTnn/+eZx99tkjY+bn5/Hss886j48fP475+Xnn8b59+3Dw4EH8wz/8g++2lEol\naVRqWhWfWUIsakjaoy+0uEsqBRtBRwm/qJ3jPycWSih2maUxRWEna+Ol9Lbj0rO8kHNelnV7wOhY\nfVVs8cLOq0Cj1Blsd19RCOcl9Ert4f/NunqcF2HE3UhWkfe5Cxi5C915ApCaQacSzzYp4zENmxEe\nTdNcbbB4r7WgPU6LFjwABveTPBr0T0rmBJ0Xl19+Ofbt24e9e/fiM5/5DK644oqRMbt378aTTz6J\nZ555Bps3b8b+/ftx//33AxhUv37yk5/EP//zP0c2ub8oiCKWFTWwdCrrWRvFnJGoUYq7tMyjY0Qt\n7sSbPRcBGplPJ0mvyoSdKg0rRutkIk6G1h+KOq/36N2BqPOrtmXbWl4Z/OWFnWeqV4zarYq7cYUd\n4C3uPL96muz4BBR4Hil6tmz/hQRa1fSYUNhNW8R5USqVHE85WY9TJu5YUYVt24UUdBShk5OrKtdT\np07hXe96F44dO4Zt27bhgQcewNzcHJ577jnccMMN+NrXvgZgINxuvfVWx7bkIx/5CABg+/btMAzD\n6c36mte8Bn/+53/uuc7Xv/71znIZ7Xbb6T1XFEzTRKfTwczMjKsyldmLZLFn7UX3/kXSmxCMCapg\nAYmQUfQt5ZEWLAjPyebQKQXXBBYsjNLq+voKf1WvAgpxft0IAdY/ibhjMG0ijd6FOH1GBF6A94ay\nOAm4zNjJgYgLAiuqYFWzuq474m5xcdFxXigKKysr0DQN9br7pPOKZOaIYtiWJMGb3vQmfPGLX3SJ\nt2l1TUgDrKih1+u5etaWSqVMijgVeRR30nthSO+6SIWdZHt4M1+vitWSsA5R1HmJOcBH0IWv9RlL\n3HlF5UYMkIOyepB9u2PItietHnYFEXEq2BxkwzAcu6iZmRlpA/u8ouqOUXRBV5wQUkywwggW1QPy\nP4dOLGrQdR2lUgmmaebWpfu7197g/D/V4s6v64Rf2lZhcaLZcIol3D1LV9/GCSoxvWpVRkWdXZaI\nOm7bS5L0qqonqyjmgEGVKhN1fmJOM4FyC+jLvMDHEHNA+Pl2SjEnqRgOVFghiB4+BR5E3Nli4Uoa\nbE7GEHJ5EXE8fFFFrVbD0tISADhFFSxyF6aoImtQylUOCboJYV50vKAD8ldKzs+H4ytTWVEDSwkU\ngcfefz1arRYajQZ23feXSW+OHB97EMAdgfHyrxuZD1caFXZMZDDhwZY98ni1iMGuuEWdTMCpYG2+\nALmYY5Q7AXzouH0rtwZ/HWE3ppgTKbXhiBxZJNBPzInoPfdrI/voIXxsDaP7pQuvS9/ov12xE3Cu\n3H9e+wGsrKxIuwTlEV3XnR/Spmk6LbBarZYj7PIWubIsq/DiTQYJugmZm5uTmgvnQdDJ2m1VKhXP\nytQiTNDl9y9VkbuwXzmJ1V4YixNXEYXTr3Tw2ImmCULPqg1EncYJMako8xGken/y4kZV94hya7B8\nY+1kyx+uaPjfUsf9Ul8VvQsh8thnPRTo2sgcuqCGw5o9pofdNE95Sdk2H4nr9Xq5vwYxxPsMXzHL\n7FAMw3CJu7jtoaaBbdvSfSjKcVdBgm5CNm7cKDUXHsdkN2lk7bZY2bxfZWrRTyQgBeIujH+dAq8q\nWEBtQ8JsNERhB6x2d+CEHrMYYdE6c1X0jQg7hagr8+lMj7lvpQ5QAtAbswtfdZDJik7YCdj60OOO\nR7lPilNMJsBY9NQ5nmN42EELUOgtpvineBl4/Kbflj5fhB+VPKp91XUdMzMzmJmZcRVVtNvt2NqQ\nTQvZMS7SMVdBgm5Cms2mVNBlJUIXVbstYLjfRTix/PY1E+LOz+LEIyXrek0ypw4YCDlbd0fpnFRp\nZ9S3zqz4izpezLHlyAQQHwmrDMz4XcLOq7erOOeOCTvNArphs3ghRBh7XmbPojJQ9oqmucR5GA87\nD99C2y8aF7OwU4m4ohL0est3quCLKqJuQzYtinKfCQsJugnZsGEDTpw44Xou7YIu7nZbhJvH3n+9\n81m/5v6/mf4GxC3uFP51I/PquAIKc2Yo6oBhqy2VqGO+cTJEUSemNRmV5YGoCyPmRGqrjWECCbsx\nxNzoBq3+kaSlVZ0rPKNquq2OvPrcH20xGgfhPTHdX//9vf/LSRcGoUg3+3H2lS+qmJ2ddebdRdGG\nbBqovPfSuK3ThgTdhDSbTfzgBz9IejN8mUa7rbQL2Sjx21fV5/3Y+693Ljy5jNx5zKsDVqN0q/dl\nZsWhG4OK1HJnKOZEUaZsI4bheCYSvaj/1EZnQ/gLv7huJuxsDTDWyd4gX844Yk41dqRyuOT+616W\nx3eVrUcyN8435WrDnXaN6J7KInFi54Rx2mLlmUnFq6ZpjlcoL+4maUM2LdK2PWmABN2EpDnlKitq\niLvdVhr2OynCfN6WZeHb17wflmVh9998JpkNjlvcCfPqAHn6VbNWU7P9YYRMJs6CiLogzJwabJco\n7Pyicyqqi8P/G+tWI4GSeXdRirmR5/lUN1+4sjpedng9ix8kRTJ2kGjcBNWw33nftU6nBNbaSeyc\nwFdwqtpiUYRufGRFFZ1OB8vLyy5xl2Qmhypc1ZCgm5A0CTq+qME0zam32yriSSYTcarPm1m/MFiq\n+z+vu9G5QP78X/w/U91+hzDiTvG6X8EEwEXtJNkzY93AvoT1Ww0ScWNUl4frMNbIv4fltnvDZ04N\no3VeYk4lImXRq+ri4HOorM67Y8JOnPvnbKus4GICMaca75pDx9nRhOkoEagCNuQl4HvXf8A5TyzL\nctpdsSpGZlDO/rFJ/nxbLLGCs0g/KuMUr6rPW9WGbFpQhasaEnQTIhN0jGn8UlRVptZqtal3akhL\nZDJO2Odt2zY6nYHa8BLNoohjzbjZDYqNYS19vvmu33TsYf6Pz9w7vR3j8RN3EUTtALW4M6sDYTfz\ns1FRJ4vS8WKOPRZFnSjmGLyokxGk5RiPKHiYsLMlV1qrNDo3UGUaLDMnDiLk/J53qmGZsJOkTaMW\ncf953Y3o9Xro9XpYXFx0xBiLaANDccf6QMvEXa1WQ61WG6ng1DQNuq47Ux3yjErcRI3X5823IZtG\n4KBIEdiwkKCbENYpgkfTtFgrPvmiBtM0nXkQ41SmEv7IRDMAqRs7E3vsL7u5sAsdL+K63a7TMo2J\nuNnZWWd537/hJme5qY3chRF3CoPiwWtucWdVBv9sDWg85142L+pEMceQiToVa04MFrayKfiN0Xdu\nGT9WIeZGnpOIOfZecb6cJem04dUBQh3dkx004T2quXEhPgP+uwzAEQcs8tPtdrGysuKcB3wvbJm4\n4wWeWMG5vLwMy7KcCk72Wh7FXRI/oFUVs6yogom7uIoqqEuEGhJ0E8JaXsWNbJI9iwylpTI1TxE6\nPzuXTqfj3EyYeGPiGoCviGPp2VqtFujClypxN+58O4VB8eC1UXFnrhZNrJwz+Lv+ycGYXkODrQO1\nRe/vGhN1quicyOxJyyXqwqRaAbloikLMjYyVPK82f159jtsXW1cIOe710SdX/4a81IhCToSP/DDR\n1uv10G63HXEni9yx85KdX+Vy2Tkf+S42WbfnCEKS+8FXzLJrIF9UEUcbMorQqSFBFxNRiBt+Ppys\n3RYRLarIp8rOhc1TZBcYJrJ5EWeaJjqdjjMvKIyIU5G4uIuimCKEuGPC7tSFg4WWjIG4s0ruAgAZ\nfmJOfH32ZPhoHRAgLelBUDGnamMmi8wp07GsbdtIdbLHBkYs4pSr4aJpLK3HxB0zwhUjdywa3u12\nnfOO/VgS7TmYWOQjSVkXd2kSN3zFLCCvUI6iDRlF6NSQoIsA1QTNcQTdOO220kIWI3QqTz5Z5JO/\ngQBAv993zZ/Tdd15nRdxlUoF9Xo9lhtHbsXd6ntkc+7MqlvcNX8Y/Xdu7bFBVHZ53n2JjDrVOomY\nG0fIBRmvyVKuzovy5Y8r4lTI0npMHPDijv2IMk3TOe9YRN0wDNcPLPaeer3u8l6zbdtZV1q911Sk\nSdCJiBXKfBELu8aOk2GiKlc1JOgioFwuo9fruYwvg4qbSdptpY2stDwL48knS6eyGwqLIqysrLii\nAwBiFXEqcifuAhRUmFXgxVetprlX55lt+N/DcbopT3EC/tE7AFhzQi7sXNs1Zqq10hrtcmFWAU3o\nFGFVJHPoKpLIZnn0M3PWabm/g3ZFIfCC9nHVohdxKsS0Hi/u+GkPbBy7drJiI9k8Vi/vtTjShHGR\nZkHHE6SoIug8R+beIJKFzyFuSNBFACuMOOuss5znvASdLLXHfslQUUM8qEScyiOOCTlgmEpgUTi2\nPDZ3kr2fpV/5SrykjmUuxF3QallWULGamn3x1ZzAs4HN/9pD+yWTXerWnOgDq8dyaT785HrWV5ZH\nJuZ4ZNG7wBE9VaSOfW5iS6+Au/T9G6cj4lQwQcb+sXOUv9ay865cLjs/sFiEiL3Oizveey1rRsZZ\nEXQ8Xm3I+NdUP4azuM/TggRdBDSbTZw+fdol6ETCpPayStpSrmGNfkURx1IGvIhj83rYhOxKpYJG\no+H8YuQjCN1u15XqSeo4503cAcIkfyGdKFbMnnhDZegzZwNzP7I9o3MlwzvKvPbEMDTWnxm9sfTr\nkueEcWHFXCAhZ6nGBU+3ykhaxAHD+ViqaQzs+trr9dBqtRxBx9KyYlEFW44473UcI+Mkybq48WpD\npkqFZ32f44QEXQTMzc1JzYXZhSPOdluEm7BGv+wfs5rxE3FMoLFoqohXeoi3ZKDIHcYWd4BP9E5m\nh1KGMzns1M8DWl93dUE467H4pgqMI+ZYOpVFHfl9dObTWcPxAEZCgC5vOfZcwCt+GkQcu36yqnCv\naQz8hHx+zla73XYEYFhxF9TIOMlreZ7ETdA2ZKo5dHn5HCaBBF0EbNiwwRF0rNqKXSQAKKNCeSOJ\nCB2bg8iin37dMVTdGkQRZxiGI8bYnDmViFMhiju+ao/EHeIRd2IqsSxG74bP86/89Bf44zr4/zmP\nckZvkmMUJDoXRMyx+XFmbbiNlijyZGlVWTROUvyQZRHHrp1h5qLyP8x4rzte3DHhoBJ3fkbGzAic\nVeAm0TUhTdmQOFC1ITNNE+122xF5NE1piObzpcj3NyYCbNvGH/7hH+L48eP41re+hTe84Q346Ec/\nCk3TYJomZmdnk97EqWGaJrrdbuz7rCok4b2oeIJ0axAjcbwHVtS/wGXrSlOFXWI+d4wgV50AY0Rx\nN4JHUI5vlcXDxNemb5uhBR0Tc6Uue231+RpbqVukiSJO1UUiTyLONE2XPUnU5wP74ccLRnFd/PQL\nmbjj4Sf493q9qRoZ27aN06dPY8OGDbGuJ22cOnUKs7OzzvWTCfd169YlvWnTQnlSkKAbg36/j298\n4xv40pe+hC9/+cvodrt47Wtfi+uuuw579uxBuVx2JnoWSdBZloV2u41GoxH5ssOIuDBGv+yiwIu4\naUbNeDPVfr8f681sHDIh7gKM8xV3PstQCTxg2AdWVojg1SN2sGD1S2rfuezPiRN/1CTxvQ8iJEVx\nJ5uWwe8Tu+4bhhG7kbFlWVhYWECz2Yx0uWnn1KlTaDabTkaIRVVJ0OVU0J0+fRpXXXUVnnnmGZx3\n3nl44IEHsH79+pFxhw4dwm233QbLsnDddddh7969rtc/9alP4cMf/jBefPFF16+g3/u938MjjzyC\nK6+8EldeeSX++7//G9/4xjfw4Q9/2BkzrWhVmrBtG61WC2vWrIlseTKjX1nULKyIm0Y0ICyydFNa\ntg3Ij7gLwkiXCMnHL9qGjLUeU/Ps2gAohJrt8ZqENIq4NEw7YIg/rGTbpmrrJ7se8fNnDWPgQxO1\nkbFpmlhaWsLc3NzEy8oKLCrJBB2DieeCUCxBt3fvXmzcuBG333477rzzTpw+fRp33HGHa4xlhkM4\npwAAIABJREFUWbjgggtw+PBhnHvuudi9ezf279+PHTt2AACOHz+O66+/Hj/84Q/x7W9/2yXoxKbP\n//7v/47Pfvaz+PjHP+5aflzRqrQShaBTVQN7iTi/vqlB0ixpQzYhfFrNr4OQKXHn93FFkb4NuBzf\nRXjMBxRf9yMtIo6de71eL1UiTkWQ6Rde4g5wm83zLbEMw4jMyLjf76PVakmDFXlFFZUkQTcgl0UR\nBw4cwCOPPAIAeN/73oc3vOENI4Lu6NGj2L59O7Zt2wYAuPrqq3HgwAFH0H3oQx/CJz/5SVx++eUj\nyxfnRjSbTWmVa94nrYqMW1Y+jtEvb2DMN+n26tYwacutaSL2uGQmnGLFHhVUrKLqZhBV4YU2HKfq\n8RqmWb1ruX6vefVWFUijiGNFA2GLipJC9Eljwk5sQcZSr7zXHd+CLG4j4zxVuAaF2n55k0tB98IL\nL2DTpk0AgHPOOQcvvPDCyJgTJ05g69atzuMtW7bg6NGjAICvfOUr2Lp1K171qlcFWp9M0DGKeNIF\nIazRr6xbg8zol01Ojrvl1jTh7ROY1xYv7pjwLay4A4KJqbDiToHMEy9ISzDNDhhhC7MvdnpEHDv/\ngtj7ZAVVCzKZxyTfKWYaRsZFvLdQ2y9vMivo3vrWt+LkyZPOY/bl/tjHPjYyNswXoN1u4xOf+AS+\n/vWvu5btxfr167G4uDj2OvMEi0zK9p/NUzFNE6Zphjb6ldmL8JEAZhOSBxGnQmbHwIxU+chBUqRC\n3AUhiLgLyIhIE5e3ui5P0Rfyqzqttlte8Ga+rMIzDyJOhcxjst/vY3l5eeT8CyPuxjUyLloGCIBT\ndSySx2v9OGRW0PGCS2TTpk04efIkNm3ahOeffx5nn332yJj5+Xk8++yzzuPjx49jfn4eTz31FJ5+\n+mlcdNFFsG0bx48fx8UXX4yjR49KlwPAFXbn8RI3eUVMNcuMftlFf9xuDTIR12g0CuVHJHptiS75\nJO5CEFTcBR3H32+CLi8AaRRxsm4pRYA/x/jIuXj+8fPq4jAyLsr1jlG0+2lYMivovLj88suxb98+\n7N27F5/5zGdwxRVXjIzZvXs3nnzySTzzzDPYvHkz9u/fj/vvvx87d+7E888/74x72ctehu985ztj\nlYYXcR7dOEa/fLcGdmHz69ZQLpcLdxNRIbrk8zeXNLQes20bj73/evR6Pez+m88ksg2BCXqviHqc\ngn+7+j3O8UsKdk4zgVFUEadCdf6trKyE6lLBmxgHMTIuYvqR5tB5k0tBt3fvXrzrXe/Cvffei23b\ntuGBBx4AADz33HO44YYb8LWvfQ2lUgl33XUXLr30Use2ZOfOnSPLCirKVF+yIgg63iPOtm10u12n\nCCGI0S8THSqj30m6NRQN2c3FMIyp95VVRXK+e+0NjghIddQuQVgkTtaflD9+cd/EZP1TixYJDwt/\n/vFCOEgLMnb9FI2MNU1ziTsmrJm4ZmbGRRDXFKHzJpe2JUnw5je/GZ///Oddv6T5Fk95Q2X0y3u7\n8YzbrYF9fiTiJkNVeRhlJwyViAuS+i26uPNLp3p9tlEKLDaPixdxSVdU5wVRIAftUiFmLBitVssR\nONMwMk4DKysr0DQN9Xrd9Xy1Ws3l/ioolm1JEjSbTSwsLOCss85ynsvbF0xl9Fuv152LTafTARDO\n6JfdQHjPJ36ZxOTIJnRH0Vc2qjlVmZlvFyFh5sR5pdUnFXcyz8M8FxYlhVgAwaplV1ZWXAbnYuSO\nXXNlc4rZ92F2dtY5p5eXlwFEb2ScBtj3k5BDgi4ims0mTp8+PSLosp5yVRn9ennEsYgdgJGJv2xc\nt9t1ujUwQTE7O5ubC0+aEcUdu5kHFXdxT4zPu7ibtLghCnEn60qSJZ/GrCP6TPLijj8HeXHHX4sB\nONdjwH1OMzsUwzAccccid1k/vpRy9YYEXUQwQceTVUE3idGvpmnOXBDeXZ0XcXQDSQ8yE1Um7sSb\nShLVjXkRd3FVqIYRd3xklvVPpXMweURxJ4ue81MjWEYDgGOgLnapiMPIOA1QUYQ3JOgiQtUtQmZn\nkkbGMfqVdWuYmZlxfkl2u10sLS05Y+gGkm54ccd7YvFivVqtJlbdmDVxN22bEVVBDIvSAP9/e/ce\n1dSZ7g/8GwgECIo3xIqXar2gra21g5fR0XoB74CAJEGSntZTV3uWo/3NdGq7TrtOezqdtmvGrjPr\nOO3qWZ2pBCSJooiigKLVqRe8jmKtlypTblW8UQYQEnL5/eHacSfZCQFCsvfO81mraxXY6ht29t7f\nvO/zvi/stZPUG85PzAQH9gcsZpcYBvsa9GaXCl8tZMwHXIFOCO32Fwp0PuJptwi+6u5Cv97u1uA8\nMy4kJMT+fabYVyg3kGDDNZwaHh4OAPaAwHzKF+TWY+wNUj2t9OvtcR7aFShck4uYh7/ZbIbRaLTX\nItGMVX7iqmtk7qMmk8lh8ll3d6no6ULGfEBDrp5RoPORQYMGoa6uzuF7fBxy7e1Cv552a2APtXIV\nVXsa0qOLNHDcrfjP1RPHPCyYnjs+zILsMtxx7XLv/H2bxPvjPPz7geI8i9ldXWqgl0Ih7jkHcXcj\nGlxbkDHnm7k3Mx+cPYW7nixkHGhca+/Re/YxCnQ+MnDgQHz33XcO3+NDoOvpQr892a0hKirK40PB\neUiPuSGxw52YZmTxmbsQFx0d7fEGzq734dpXNtDn0CXcuQtpzrpznE3CuxDn7f6pfTlblnSft0Gc\nzXlSk692qehqIeNAhzv2M4lwo0DnI+5q6AIR6NytEedpoV92iPO0WwNz8+ltUbynYMB0+wfDQpn+\n1NMQ5w57+IZ9DgHwIhg4hLuvvuj13ze2sAN7yv5fr/+e3vDl/qnO4c7d3sAU7nyrL88hV7hjRlW8\n3aXC3ULG7e3tDjV+/r4/M8Ot9F50jwKdjwQ60LkLccxNwpvdGrpa6NfTUFxvOG84z3T7Mz16fK7p\n4Dvm4WEymRzOYU9DnDueziEv9pX999eRmvQZpLV3ce13o7z+c2MLO/qwVd5xV9foy3PI7olnL6Xx\n8OFDAPwI6ELG3J+Zni/muvD1OXQOd2azude7VLAnaZjNZphMJvzrX/+yhzt/9crTDNeuUaDzkUGD\nBrmdFNFXhZzeLPTLxoQ49icdrhDHPPz9veUW057IyEjObat8vbOBWPVkKM5XuM6hc49BIIduzKNi\nMfGPtUDoo3//2m9GuBzDlxDHFQD8McOYwp3vOO+84a9Z4uxwxz6H7HDH/NxTuGMHPPaHs0AsZEwT\nIrpGgc5HYmJi0Nzc7PC9vg5x3i7029VuDeyaCfZuDYHcN5V9Q/LlzgZiFcgQ54674aDW1la/7ivr\nycTP6h2+7hw1xM2R8MtwK7snDkDA90/tKtyx7z10LT7Ct5032OeQ3XPH1C+z17rztEsF86xxDnf+\nWsiYeui6RoHOR5iZRc6YYdfevOl6s9Av4H63Bq4Qx8f1qZyLgGmm7CN8DHHuOIc751l6/gh3xQd/\ng9SkzzweE1Z7z2Oo6wtcS/3wcestT+GOL5NiAsXbGap8wHUOu9qCjHmmsNe6Y4c7fyxkzDXDlTii\nQNfHelpH19uFft3tm8recov5FMXHEOdOsM+UFVKIc8c5oDOvp6Ojg7e9r77unWMvE8HnEOeOu3DH\npxnPfa0nM1T5hmsLMiaMsa9F5nniLtx5WsiYvdZdbxYyZoaBnQnld+0PFOh8yN0by9tA15OFfrl6\n4thvembHBjFuuRUsM2XFEOLc4Qp3zIy6vgp35lGxkDbc99nf5y2u/VOFFOLcCaZw58sZqnzj7RZk\nzLlmL2RsMpm6DHe9XciYaui6JukibPBrVVyeW7hwIXbs2IGwsDD795ieI6b72hnXQr/MReMuxHW1\nWwP7weFcACv2C4KrmFyIM2XdhTihvY6e4trtwFc1OalJn3UZ6NjDrr3pnWNfi+zV/YPpWnS+Fwkt\n3LmboBLoddn8xXnJKmaiHPtexA537OWvnEeJGOzeQHbJj6ff6cOHDyGRSBAZGenw/fDwcMG8l3zE\n7YulHjofYpYuiY2NtX/PecjVFwv9cu3WIJQ6nL4m5JmyYu6J6y7noXWm5865zqcn721p7d1H/xPa\nN79TIdVT9SWh99wFaoYq33AtXeKu/pUd8LrapaK7Cxm7G3Ilj1Gg8yF3gY4d4Hqy0C/7xuhptwax\nDOH4ihBmylKI6xp7MVPnukn2UFCgz6Nzj6LQ6qn6klDCHd9mqPKNu/pXpp6OfR65wh3XLhXeLmRM\nQ65do0DnQwMHDkRTUxMAx544poehuwv9cu3WwLXlViCXNRAKPs2UpRDXc1xF3H05KcbTcKsYiuID\ngW/hjnpUe8b5ntqTLci6s5Ax08HBDoRMO8gjVEPnQx999BFCQkJw5coVPP/888jOzrYv4BsREeFy\nvLsQ57zQr/PDn70RM+kdrk/kffEwCfaauL7GNWvU03nMmPhOl0OunaOGuAQ65xDHDA/xdRhfSPxZ\nc+cujAe6x14MuHY2YT+zmN8veySKK9w5/53Nzc2QSqX2US4m+Mnlcr+/xgCjGrq+8vDhQ5SXl2PX\nrl3YtWsXJkyYgFWrVmHRokWIioqyF0MznHdrcLfQL3Mx+Hu3hmDTlzNlqSfOfzydR3axdXce1mG1\n9wC43z6NzqNvcS2A68ueOzHPUOUT5zUnPfXAdmeXCgD2XZDYy6EEYaBzS9Q9dE1NTVAoFKipqcGT\nTz6J7du3IyYmxuW4srIyvPHGG7BarVi7di02bdpk/9n//u//4vPPP4dUKsXy5cvxySef2H/2pz/9\nCR9++CESExORnp6O0NBQtLa2Yt26dfZj2J8Au9qtgd3tzzWTiPhHb2bKUk8cfzj3+ACPt63Kmvxu\nlz10hqoPXB7+dB4Dg2vSlzfhLthnqPKN83nkqoF17rljnpNtbW2IiYlxOG/MdRlk3L7hRR3oNm3a\nhMGDB+Ott97Cp59+iqamJodABjx680yYMAGHDh3C8OHDkZiYCL1ej4SEBBw5cgR/+MMfsH//fkil\nUty7dw9DhjxezuDmzZsYMGAABg8eDACoqKjA0aNH8eabb9pvJMwDhT3DkunxYa/1wy6kpuEb/uDq\nnXEeYqMQx3/OvTMvJ37cZaDbeupth+BA+MGbcMc1Q5XOI79wrcvoHO6cz3VERIS9Z4/pxaNA95io\nh1yLi4tx9OhRAMBLL72EF1980SXQnT59GuPHj8fo0aMBAEqlEsXFxUhISMAXX3yBt99+294tzA5z\nAPDUU085fB0REYGqqip7gGPebMwwENNFHBoaag98VEjNb55myjJDAcxOHjR8w1/Ow0CGyx9C8fR7\nHkNdv379/NhC4i13w7JWq9V+bw3mpZuEwt0Ep4cPHzrcW9mTCYHHOx51dHTg9OnTSElJCfAr4Q9R\nP3nu3LmDuLg4AMCwYcNw584dl2MaGhowcuRI+9cjRoxAQ0MDAOD69ev4+9//jpkzZ2L+/Pk4e/as\nx39v+PDhkMlkWLZsGT7++GPcvHkToaGhqK2txZYtW3Dv3uOaHKYrmfm0QTccYWIvokkzjYWBmahE\nhI9rEhnzHxEOdv0kc20y5/DChQvYtm2bfQWJkydP4o033kBaWhouXbrksFtSsBN8D11SUhIaGxvt\nXzNB6fe//73Lsd29iZvNZjQ1NaGyshJnzpxBVlYWqqur3R4/duxYbN++HRaLBVu3bsXatWtx69Yt\nmM1mJCcnIy0tDf3797cvNsx8umxtbbUP5dEsK37hmtXo3BMXjHvKCpHzMJwnfzv5FlpbW2nonIe8\nWS7G1xMqSN9gX5MA7MtwMUPjTDgvLi7G22+/jfDwcEyZMgWbNm1CcnIyXZdOBB/oDh486PZncXFx\naGxsRFxcHG7fvo2hQ4e6HBMfH4/a2lr71/X19YiPjwfwqLcuPT0dAJCYmIiQkBDcv3/fXjPH5aOP\nPoJOp8ODBw+Qnp6OpUuX4s6dOzAYDHjnnXeQlZWFZcuWITIy0mEIyHkPS19tc0S6z5sQxxYse8oK\nkaeFYj3p37+//T3Q0dFBy1oEWHdnqPblbFnSO+zFgz0t3nzv3j3s3LkTRUVFiIuLw9/+9jdYLBYU\nFxdDpVJhypQpeP3116FSqQL4avhF8IHOk5SUFGzduhWbNm1Cbm4uUlNTXY5JTEzEjRs3UFNTgyee\neAJ6vR46nQ4AkJaWhsOHD2PevHm4fv06Ojs7PYY5ABg8eDD+7//+DzNnznS40bz88suor6/Htm3b\nkJKSgokTJ0KpVOKXv/ylQxE982an3h7/6m6Ic8d5wVSTyWRfaFOIe8oKEVexdXcXivW0EDWFO/9w\nN0M1Ojq6R9ckhbvA4epV5bomOzo6UFpaCoPBgLa2NigUChQXF2PgwIH2YxQKBTo6OnDo0CGYTKZA\nvBzeEvUs1wcPHiArKwt1dXUYPXo0tm/fjgEDBuDWrVt49dVXUVJSAuDRsiUbN260L1vy9ttvA3i0\n5Mgrr7yCCxcuQCaTYfPmzZg3b16v22Wz2XDhwgXk5ubi5MmTmD9/PlQqFcaPH+9wHFd3NE239x13\nIc7XocubmbKkd9j7vVosFq93/8iY/J+c39/5/Uec3+faVYAPW4+Jib9mqPZ0KRTiHXe9qs73V6vV\nisrKSuj1ely6dAnLly9HTk4OxowZQ+eBW3AuWyIEZrMZ5eXlyMvLw+3bt5GamorMzEyHnkCuC4Pq\n7XrGXyHO23+fent6zhfhiivQuQtzznoaIokrf+3Y4g6FO9/h6ohwDuQ2mw3V1dXQ6XSoqKjACy+8\nAI1GgxkzZtCH3K5RoBOC5uZmFBYWwmAwICoqCgqFAkuWLIFMJrMfw97fjlm7jurtPAt0iPPULurt\n6R7n31lvAzHXFmDeBjo2rmHe8PBwCgQe8PX9T+Gu+7jq4rh+Zw8ePMCuXbtQVFSEQYMGYc2aNVi+\nfLnDM450iQKd0NTU1CA/Px8lJSWYMmUKlEolZsyY4XBx2Gw2+yehQHyq5TO+hjh3At1DwWd92avp\nq0DHRufSPaH1UFO4c4/rXHJ1LhiNRhw4cAB6vR4///wzVq9eDYVC0WU9OnGLAp1Q2Ww2nD17Frm5\nuTh79iwWLVoElUqFMWPGOBxH9XbCC3HuOD9EgnGmrL923+iLQMdGgcD7Wiq+o3PpOlHFU13cuXPn\noNPpcP78eSxevBhqtRrjx48Pmt9VH6JAJwYmkwmlpaXIz8/H/fv3sWrVKqSnpzvMAAq2ejt3n/jF\nMOGgN3vKClGgHvzsOjpfhjln7oK6GBekFvseqsEW7ryZqGKz2VBTUwO9Xo/y8nI8++yzUKvVmDNn\njijOOY9QoBObpqYmbN++3T5zV6lUIikpCeHh4fZjnOvt+FKj0ltiDnHuiHWmrHOIC0Ro9VegYzBh\nh6k5Yi+RIvRe2GDcQ1Ws4c65Ls5dXWhzczOKiopQWFiIfv36Yc2aNUhJSUFEREQAWy9qFOjErLq6\nGnl5eSgtLcXzzz8PlUqFF154weGiE3pdD9dkELGHOHeEVofkjCvEBTLQ+DvQsbn7XQipJ0vo9xZf\nslgs9mtTiL8Lb+viOjs7UVFRAZ1Oh7t37yIjIwMqlQqxsbEBbH3QoEAXDGw2GyorK5Gbm4uLFy9i\n8eLFUCqVGDVqlMNx7AcIwN96O3czGoMxxLnD15mCXLjed3zovQlkoGMTUq2ZkN53gSKUoNuduriL\nFy+ioKAAZ86cwcKFC6HRaJCQkMCr1xMEKNAFG6PRiJKSEuTn56OlpQUZGRlYtWoV+vfvbz+Gj/V2\nFOJ6jo8PEK7hKObDA18eAszEiECGOWf+mhTS0zYJsWc4kPi4rA172N9TXVxDQwMMBgP279+PhIQE\naDQazJ07N+AfxIIYBbpgdv/+fej1ehQWFiI2NhZKpRKLFi2CVPp457dA1ttRiPO9QM6UdX5Q8CFY\ndiVj8n/yKtCxBbJmVEi9hkLBFe78fa/tqi6upaUFu3fvRmFhIWQyGbKzs5Gamgq5XN6n7SNeoUDX\nXfX19dBoNGhsbERISAheffVVbNiwweW4DRs2oLS0FHK5HFu3bsXUqVMD0FrvXb9+HVqtFhUVFUhM\nTIRSqcTUqVO7rLfzda8KhTj/8NdMWT72DnYHnwMdm7taUl/2kol9hiqf+CPceVsXZzab8c0330Cn\n06G+vh6rVq3CmjVrEBcXx9trWKzP6S5QoOuu27dv4/bt25g6dSpaW1vxwgsvoLi4GAkJCfZjSktL\nsWXLFuzbtw+nTp3Cxo0bUVlZGcBWe89qteLYsWPQarW4cuUKli5dCoVCgfj4eIfjmE/n7Nl4Pb2x\nU4gLLF/PlA1kTwPx/a4ZwThDlU98fT0x17qnnlWbzYbvvvsOBQUFOHHiBF588UVoNBo888wzgriG\nxf6cdsPtiZG6+0GwGzZsGIYNGwYAiI6OxqRJk9DQ0ODwRikuLoZGowEAzJgxA83NzWhsbERcXFxA\n2twdISEhmDt3LubOnYv29nbs2bMHv/3tb2E0GpGZmYnU1FRER0cjNDQUoaGhkMlk9nDX2trqdb2d\nu4dOZGQkhTg/k0gkkEqlkEqlDp/a29vbvQ4DXMXwMpmMQlwAML2t4eHhDuelvb3d65IJrp7VyMhI\nwfSsiklISAhkMhlkMpn9vBiNRofr09vzya6Lk8vlLnVxjY2NMBgM2Lt3L5566iloNBp89tlnggvv\nYn9OdxcFOi/8+OOPuHDhAmbMmOHw/YaGBowcOdL+dXx8PBoaGgT3RomMjIRCoYBCocCdO3eg0+mw\nevVqxMfHQ6lUYv78+QgNDbWHgYiICPuwD9fDw12Ii4qKoocET7CXCukqDND55D92uOsqDFAo57/u\nhDv2+bRYLJBKpZyhvK2tDXv27MGOHTsgkUigUqlQXl6Ofv36BfCV+o7Yn9PeoEDXhdbWVmRmZuLP\nf/4zoqOjA92cPjd06FBs3LgRGzduxPfffw+tVouPPvoIv/zlL6FSqexd8cxDn7nZdHR0wGq12m8w\n9NAXDq4wQOdTuLjCAHM+Q0JCHIbz6Hzyn6fz2dX1abFY8O2336KgoADV1dVITU3FV199hfj4eFGd\n92B7TrtDgc4Ds9mMzMxMqNVqpKamuvw8Pj4edXV19q/r6+tdatCEbPLkyfjkk09gtVpx5MgRfP75\n57hx4wZWrlyJ1atXIzIyEnv37sWtW7ewbt06+ydCs9kMq9UKm80Gm80mqhuHmDE1dhaLBVar1X4+\nme+Fhobav0/4j5ncwFyLzPlkznNISAhCQkJoeFVAmHNqs9ns589qtcJsNuO//uu/sGDBAixYsADV\n1dXQ6/U4evQo5syZg9/+9rcuk9/EItif02wU6Dx45ZVXMHnyZGzcuJHz5ykpKfjLX/4ChUKByspK\nDBgwQJTduCEhIfYbxa1bt/Df//3fmDVrlr0INScnB/3797ffLNjF90ajkRfr2xFu7tY7i4iIsNc4\nsmc9trW1iX5PWSFzN0M1Ojra4Vwx9bDt7e28XR+QPOJNXVx7eztiY2Px+9//Hv/2b/+G2NhYvPzy\nyzh69CiioqIC2Pq+R8/px2iWqxvHjx/H3LlzMWXKFEgkEkgkEvzhD39ATU0NJBIJ1q1bBwBYv349\nysrKIJfL8fXXX2PatGkBbnnfqKqqwnvvvYdvvvkG8+bNw+rVqzF9+nSUlJSguLgYY8aMgVKpxNy5\nc11mUYlxP1kh683aYmLdU1boejpDlb2vLN928AhmXHWOXOvFtbe3o6SkBNu3b0dnZycUCgVmzJiB\niooK7NixA1evXkVKSgr+9Kc/YfDgwQF8RX0jSJ/TtGwJ6Z1//vOfOHbsGFJSUhATE+Py86qqKmi1\nWnz77beYO3culEolJk2a5HCMP9a3I9z6Ys9Q2jkgsHy99h/f9tgNNuwPS56uJ4vFghMnTkCn0+Ha\ntWtYsWIFcnJyMGrUKJfzXl9fj6KiIrz22msICwvz90sifYMCHfEPi8WCiooK5OXloba2FqmpqcjI\nyMDQoUNdjmOvb0dDeL7H7n1hryPYFw9o2tvTP/z1e+YKd3SN9g12iHP3e7bZbPjhhx+g0+lw+PBh\nzJw5E2q1Gr/4xS/ofAQfCnTE/1paWrBr1y7odDqEhYUhKysLy5cvR0REhP0Y5yG80NBQ6uXpJXfb\nfvmrJ1Tou0bwTaB7Qmn7L9/zZh9VALh37x527tyJ3bt3Y+jQoVCr1ViyZAnCw8MD1HLCAxToSGDV\n19cjPz8fe/fuxcSJE6FSqTBr1iyXT6HUy9MzziGOLyEqkHvKChlfQ5RzuGR/AKNw55m3dXEdHR0o\nKyuDwWBAa2srsrKykJWVhYEDBwaw9YRHKNARfrDZbPjHP/4BrVaLkydPYsGCBVCpVBg3bpzDce7q\n7SgIPCaknjB/7SkrZELbQzXQPYdC4G1dnNVqxalTp6DT6XDp0iUsW7YMOTk5GDt2LP0uiTMKdIR/\nOjs7ceDAAeTl5eH27dtIS0tDRkaGy2wsqrd7jGu/R65P+XxGM2UdiWEPVV/vKyt03tyzbDabfb24\ngwcPYtq0adBoNJg5c2ZQXgfEaxToCL81NzejsLAQer0ecrkcCoUCS5YsgUwmsx/j7addsWEWDjWZ\nTLBYLKIaig7WXh4h9a52V7CWTjjXxbkbVXjw4AF27dqFoqIiDBw4EGvWrMGKFSsc7nWEeECBjgjH\njz/+iPz8fOzbtw9TpkyBSqXC9OnTHR4GYn9oiP31cRH7axb76+Mi5g8jgPd1cSaTCQcOHIBer0dT\nUxMyMzOhVCpFuTYc6XMU6Ijw2Gw2nDlzBlqtFmfPnkVSUhKUSiXGjBnjcJy3n4z5joatHhNLD1aw\n9kBy4SoXEGK4605d3Llz56DX63Hu3DksXrwYarUa48ePF9TrJbxDgY4Im8lkQmlpKfLy8vDgwQOk\np6dj1apVLjO/hFZvRw/8rgltpixfZ6jyiRADu7d1cbW1tdDr9SgvL8czzzwDjUaDOXPo+/7SAAAY\n00lEQVTm0LknvkKBjohHU1MTDAYDduzYgYEDB0KpVCIpKclhJXQ+19txLf0QzJMCvMXnmbJCm6HK\nJ3xdcgfwfrZ9c3MzioqKUFhYiOjoaKxZswYpKSmIjIwMUMuJiFGgI+J08+ZN5OXloaysDNOmTYNK\npcK0adO6rLfz98xQrpmd1GvTc3yZKSuGGap8EuhFsQHvax07Oztx6NAhFBQU4M6dO8jIyIBKpUJs\nbGzAgygRNQp05LG1a9eipKQEcXFxqKqqcvn50aNHkZqairFjxwIA0tPT8e677/q7md1is9lw8uRJ\n5ObmoqqqCkuWLIFCocCoUaMcjvNnvR0NvfmHv4ethThcKDT+3LaO+fe82bHGarXi4sWL0Ol0OHXq\nFBYtWgS1Wo1Jkybx+tyL8Z4fxCjQkceOHTuG6OhoaDQatxf35s2bsWfPngC0rveMRiNKSkqQn5+P\n1tZWe71d//79HY7ri3o72uA8sPpqJmkwzlDli768pryti2toaIDBYMD+/fsxceJEvPTSS5g7d65g\nrmmx3/ODjNsbjtSfrSD8MGfOHNTU1Hg8pougz2symQwZGRnIyMjAvXv3oNfroVQqMXToUKhUKixc\nuBBSqRShoaEIDQ2FTCazfzrv6Ojodg8Puzehs7MTABAWFga5XC6YG75YMA/l8PBw+zkxGo1ob2/v\ndk+au56/qKgoCnF+JJFIIJVKIZVKERERYQ9hbW1tPer15uph5bpWW1pasHv3bhQWFiI8PBzZ2dmo\nqKiAXC7vi5fZp8R+zyePUKAjnE6ePImpU6ciPj4ef/zjHzF58uRAN6lHhgwZgvXr12P9+vW4du0a\n8vLy8Mknn2DGjBlQKpV47rnnHB4Y7J4YJgS4q7fjKuaOiorya70PcS8kJAQymcwe2Jlz6qnWzd0w\neUREBA2T8wBXuDOZTDAajR7DHVcPq0wmc+lhNZvNOHLkCAoKClBfX49Vq1ZBq9Vi2LBhor+mxXLP\nD2Y05BqkampqsHLlSs7u99bWVoSEhCAqKgqlpaXYuHEjrl+/HoBW9g2r1Ypjx44hNzcXV69exbJl\ny6BQKDB8+HCX49j1dkywYwrh+TYjj3TN3WzU0NBQe28czVAVHq6Z40wPu9ls9lgXZ7PZ8N1330Gn\n0+H48eOYN28eNBoNpkyZIqprOpjv+SJDNXTEkaeL29mYMWNw7tw5DBo0yA8t86/29nYUFxdj27Zt\nMJlMyMzMRGpqKqKjo+3H3Lt3D3K53N4TB8D+CZ+GVIXLYrHAaDTah8nZw7UU5ITLbDbDaDTCbDYD\neNRTGxISgs7OTgwYMADAoxDX2NgIg8GAvXv3YuzYsdBoNFiwYAGkUnEOXNE9XzSoho44stlsbmsm\nGhsbERcXBwA4ffo0bDabaC/syMhIKJVKKJVKNDY2QqfTITMzE0OGDMHo0aNRWVmJGzdu4Ny5c4iJ\niXHooWttbeXV+naka+7qp0JCQuxDrS0tLXReBYbrvEZHR9t76M6dO4dVq1Zh9uzZSEhIwKVLlyCV\nSqFSqVBeXo5+/foF+iX0Obrnix8FuiCUnZ2NI0eO4P79+xg1ahQ++OAD+yyvdevWobCwEF988QXC\nwsIQGRkJg8EQ6Cb7RVhYGPr16weZTIaKigpMnDgRQ4cORU5ODm7fvo0hQ4YAePSJv7v1diRwvK2f\nYmqwuM4rzWjlH2aYlVlqxN15DQ0NhdFoRGpqKn7++WccOHAAdXV1WLZsGWJiYhwWJBcruucHBxpy\nJQSPhlXHjRuHRYsWQalUYtmyZYiKioLFYsHRo0eRm5uL6upqrFixAqtXr8awYcMc/jxXvR0tVRI4\nvlqbjtac4xd3C0pz1cVduXIFer0eR48exezZs6HRaPD8889DIpHg3r172LlzJwwGA+7cuYNLly7R\n+SRCQTV0hHTl4cOHiIqKcvvztrY2FBUVoaCgAACQlZWFFStWuPwZ9pZjtJiw//T1Qs5C21NWTLxd\nL+7u3bvYsWMHiouLMWLECKjVaiQnJ3vshevquieEZyjQEeJLt27dwrZt27B7926MHTsWKpUKv/rV\nr1weMP7cwSAYBWIPVT7vKSsm7vZRdV4WqL29Hfv27YPBYIDJZIJSqURmZiZiYmIC2HpC+gwFOkL6\nysWLF6HVanHs2DHMnTsXKpUKCQkJDsew67IsFgukUinV2/UCX/ZQ5cuesmLBVRfHVb9otVpx/Phx\n6PV6XLlyBStWrEBOTg5Gjx5N1xMROwp0hPQ1s9mMiooK5OXlob6+HikpKcjIyMDQoUMdjqN6u57h\nez0b9cj2DNdQubu6uB9++AE6nQ7ffPMNpk+fDrVajcTERArPJJhQoCPEn1paWrBz507o9XqEhYVB\noVBg2bJliIiIcDiO6u08E+oeqkJttz+xQxwAt0PlzASGoqIixMXFIScnB0uXLkV4eHggmk1IoFGg\nIyRQ6uvrkZ+fjz179iAhIQEqlQqzZs3qst6OGboLtgAgtp4uvvcs+pO3dXEdHR0oKyuDXq9HW1sb\nsrKykJWVhYEDBwaw9YTwAgU6QgLNZrPhH//4B3Jzc1FZWYkFCxZApVJh3LhxLscxQ7JWqzUo6u36\neoYqXwTjTNnu1MWdOnUKer0eVVVVWLp0KdRqNcaOHSva9z0hPUCBjhA+6ezsRHl5OfLy8tDY2Ii0\ntDRkZGRg8ODBDseJud4uEDNU+ULsM2W7UxdXXV0NvV6PgwcPYtq0aVCr1S492IQQOwp0hPBVc3Mz\nduzYAYPBALlcDqVSicWLF0Mmk9mPcQ4AQu7B4ssMVb4Q00xZb+vimpqasGvXLuzatQsDBw5EdnY2\nVq5c6fCeJ4RwokBHiBD8+OOPyMvLw/79+/Hss89CqVRi+vTpLr0aQqu3ozoy7wixftDbc2symXDg\nwAHo9Xo8ePAAq1evhkKhsG+pRwjxCgU6QoTEZrPh9OnT0Gq1OH/+vH1LsjFjxrgcx9d6O5rp2Tt8\n/v11py7u3Llz0Ov1OHfuHJKTk6FWqzFhwoSAvwZCBIoCHSFCZTKZsH//fuTn5+PBgwdIT09Heno6\nBgwY4HAcH4YyhdjDJAR86OHsTl1cbW0t9Ho9ysrKMGXKFKjVapedVAghPUKBjgSPtWvXoqSkBHFx\ncaiqquI8ZsOGDSgtLYVcLsfWrVsxdepUP7eyZ5qammAwGLB9+3YMGjQISqUSSUlJDntV+rveLlhm\nqPKFv2fKst9LgPu6uObmZuzevRuFhYWQy+VYs2YNVq5cKYh9UsV8zyCiQ4GOBI9jx44hOjoaGo2G\n8+ZcWlqKLVu2YN++fTh16hQ2btyIysrKALS0d27cuIG8vDyUl5dj2rRpUKlUmDZtml/q7YJ5hipf\n9OVMWZvNZv97PfUIdnZ24tChQ9DpdGhsbERGRgZUKhViY2MF1SMbLPcMIgoU6EhwqampwcqVKzlv\nzq+99hrmz58PhUIBAJg0aRKOHDmCuLg4fzfTJ2w2G06cOAGtVouqqiosWbIESqUSI0eOdDmOXW/X\nk2E7PgzrEle+mCnrXBfnLvxbrVZUVVWhoKAAp06dwsKFC6HRaDBp0iRBhThnwXTPIILm9iKT+rMV\nhPBBQ0ODQ9iJj49HQ0ODYG/OEokEs2fPxuzZs9HR0YGSkhJs2rQJbW1tyMjIQFpaGvr372/vwQkP\nD7cHs/b2dgBwCHfOuOq3IiMjeTHxgjwikUgglUohlUodemXb29s91jG6q4uLiopy6eltaGjA9u3b\nsW/fPkycOBEajQZ//vOfgyLMi+2eQcSJAh0hIhIREYHMzExkZmbi3r170Ov1UCqViIuLg1KpxMKF\nC+29NhEREZDJZPYHeltbm73+TSqV2r/PzGKUyWS8mGFJPGOGv8PCwhxmyra3tzvUNjqvFxcdHe3S\nm9fS0oLi4mIUFhYiLCwM2dnZqKiogFwuD8RLI4R4QIGOBJ34+HjU1dXZv66vr0d8fHwAW9Q3hgwZ\ngvXr12P9+vW4du0atFotPvnkE8yYMQNKpRLPPfecQ89OWFgYOjs7YTQa0dHRYQ8G/fr1o7o4gWL3\nylosFnR0dODhw4cA4DB5hd3LZjabceTIEeh0OtTV1SEtLQ25ubkYNmxY0Ib5YLlnEGGjQEdEyWaz\nwV19aEpKCv7yl79AoVCgsrISAwYMEP3QycSJE/HRRx/hww8/xLfffou//vWvuHr1KpYsWYIJEyag\ntLQUBw8exIkTJ9C/f397D53JZEJraystBCxQXHVxzHCq2WzGmTNnsG7dOmRkZGDWrFk4fvw4jh8/\njnnz5uGdd97BlClTguZ80z2DCB1NiiCik52djSNHjuD+/fuIi4vDBx98AJPJBIlEgnXr1gEA1q9f\nj7KyMsjlcnz99deYNm1agFvtPzabDZcuXUJubi5yc3MhlUoxffp0LFy4ECqVCtHR0Q7Hcy1bQRMh\n+MvdMjLh4eEudXG3b9/G1q1bUVlZiVOnTiE2Nhavvvoq1qxZ4zKpRszonkEEhGa5EkKAu3fvYv78\n+WhpaUF2djays7MxZcoUNDY2oqCgAEVFRRg5ciSUSiVefPFFh9BG683xm7frxbW1tWHv3r3YsWMH\nbDYbVCoV0tPTIZfL8fe//x0FBQXYuXMnZs2ahb179wZNDx0hAkGBjhDyeEuxxMREtyHs8uXL0Gq1\nOHLkCGbPng2VSoWnn37a5e8R2n6yYuTtUjQWiwXHjh1DQUEBbt68iZSUFKxZswYjRozgPF9GoxGX\nL1+mXihC+IcCHSGkeywWC44cOQKtVovq6mqsXLkSmZmZGDZsmMNxvljfjnjP2zBts9lw9epV6PV6\nezhXq9Uui08TQgSFAh0Rh8uXL6OoqAhJSUn22Zp6vT7QzRK9trY2FBUVoaCgABKJBKtXr8aKFStc\nt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0df356fb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot2D(x, y, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ah! The wonders of code reuse! Now, you probably think: \"Well, if I've written this neat little function that does something so useful, I want to use it over and over again. How can I do this without copying and pasting it each time? —If you are very curious about this, you'll have to learn about *packaging*. But this goes beyond the scope of our CFD lessons. You'll just have to Google it if you really want to know."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn More"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To learn more about the role of the Poisson equation in CFD, watch **Video Lesson 11** on You Tube:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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bEqvqyDqzzi4QnqAwB/uZbvzK6LDWwPPQKgd2J30H4imq1ebZQ+85lRLAzL01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\nREQERED/2Q==\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/ZjfxA3qq2Lg\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f0df0b58f98>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('ZjfxA3qq2Lg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    div.cell{\n",
       "        width:800px;\n",
       "        margin-left:16% !important;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    h3{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "        margin-top:12px;\n",
       "        margin-bottom: 3px;\n",
       "       }\n",
       "\th4{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "       }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\t   \n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 135%;\n",
       "        font-size: 120%;\n",
       "        width:600px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\";\n",
       "\t\t\tfont-size: 90%;\n",
       "    }\n",
       "/*    .prompt{\n",
       "        display: None;\n",
       "    }*/\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 50pt;\n",
       "\t\tline-height: 100%;\n",
       "        color:#CD2305;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\t\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: #CD2305;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }  \n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
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  {
   "cell_type": "markdown",
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    "> (The cell above executes the style for this notebook.)"
   ]
  }
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